{ "cells": [ { "cell_type": "markdown", "id": "separated-apollo", "metadata": { "tags": [] }, "source": [ "# The Daring Landscape of Probability Distribution Functions\n", "\n", "Once you start venturing past the safe havens of the normal distribution, things can start looking scary quickly.\n", "To try to grant you safe passage, this post will provide a coarse map of the distribution landscape which can be obtained from [Wikipedia](https://en.wikipedia.org/wiki/List_of_probability_distributions).\n", "\n", "It will attempt to do so by creating a network of probabilistic distributions where each node corresponds to such a distribution and an edge is drawn\n", "from one node to another if they are \"related\".\n", "As a heuristic for determining whether distribution $D_1$ is related to $D_2$ we take the binary observation whether $D_2$ is mentioned in the summary of $D_1$ on Wikipedia." ] }, { "cell_type": "code", "execution_count": 1, "id": "hearing-scotland", "metadata": { "tags": [] }, "outputs": [], "source": [ "import re\n", "\n", "import pandas as pd\n", "\n", "import requests\n", "import wikipediaapi\n", "from bs4 import BeautifulSoup\n", "\n", "import graphviz\n", "import networkx as nx\n", "\n", "import seaborn as sns\n", "\n", "from tqdm.auto import tqdm" ] }, { "cell_type": "code", "execution_count": 2, "id": "conservative-fortune", "metadata": { "tags": [] }, "outputs": [], "source": [ "DISTRIBUTION_BLACKLIST = [\n", " 'probability distribution',\n", " 'continuous probability distribution',\n", " 'discrete probability distribution',\n", "]" ] }, { "cell_type": "markdown", "id": "extra-anime", "metadata": { "tags": [] }, "source": [ "## Obtaining distribution associations from Wikipedia\n", "\n", "To create the distribution map, we first obtain the [list of all \"known\" probability distributions](https://en.wikipedia.org/wiki/List_of_probability_distributions) from Wikipedia.\n", "Subsequently, we link distributions if they mention each other in their respective article summaries.\n", "\n", "The `wikipedia-api` Python package sadly does not allow to extract hyperlinks from the summary of an article only.\n", "This leads to many false positives as very often a whole bunch of not quite directly related distributions are mentioned in the appendix of an article.\n", "In particular, the `link` property of a `page` object returns links from the whole page, and the `summary` property strips away the metainformation of what is a link and what is not.\n", "\n", "\n", "So we have to write our own custom crawler instead." ] }, { "cell_type": "code", "execution_count": 3, "id": "severe-freeware", "metadata": { "tags": [] }, "outputs": [], "source": [ "wiki = wikipediaapi.Wikipedia('en', extract_format=wikipediaapi.ExtractFormat.HTML)" ] }, { "cell_type": "code", "execution_count": 4, "id": "innocent-tribute", "metadata": { "tags": [] }, "outputs": [], "source": [ "def get_related_distributions(distribution_name, verbose=False):\n", " if verbose:\n", " print(f'=== {distribution_name} ===')\n", "\n", " # retrieve page source\n", " page = wiki.page(distribution_name)\n", " if not page.exists():\n", " return []\n", "\n", " resp = requests.get(page.fullurl)\n", " soup = BeautifulSoup(resp.text, 'html.parser')\n", "\n", " # find main content\n", " res = soup.find_all('div', attrs={'class': 'mw-parser-output'})\n", " assert len(res) == 1\n", " main_content = res[0]\n", "\n", " # extract links in summary\n", " link_set = set()\n", " have_observed_table = False\n", " for child in main_content.children:\n", " if verbose:\n", " print(child)\n", " print('-' * 80)\n", "\n", " if child.name == 'table':\n", " # this makes sure we don't break immediately if the first child is a div (e.g. containing \"For other uses, see [...]\")\n", " have_observed_table = True\n", " if child.name == 'p':\n", " tmp = [\n", " link.attrs['title'].lower()\n", " for link in child.find_all('a')\n", " if 'title' in link.attrs\n", " and link.attrs['title'].lower().endswith('distribution')\n", " ]\n", " link_set.update(tmp)\n", " if child.name == 'div' and have_observed_table:\n", " break\n", "\n", " return sorted(link_set)" ] }, { "cell_type": "code", "execution_count": 5, "id": "common-thumb", "metadata": { "tags": [] }, "outputs": [], "source": [ "# at a later point we might be interested in obtaining detailed information about each distribution\n", "# unfortunately, many math notation blocks are images and not text...\n", "\n", "# table_list = pd.read_html(wiki.page('Bernoulli distribution').fullurl, match='Parameters')\n", "# assert len(table_list) == 1\n", "\n", "# df_overview = table_list[0]\n", "# df_overview" ] }, { "cell_type": "code", "execution_count": 6, "id": "catholic-scope", "metadata": { "tags": [] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "5e6934c7b858464aba6167901d55166e", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/561 [00:00\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
nodedegreein_degreeout_degree
0normal distribution53494
1exponential distribution22175
2beta distribution22157
3gamma distribution20164
4pearson distribution19415
\n", "" ], "text/plain": [ " node degree in_degree out_degree\n", "0 normal distribution 53 49 4\n", "1 exponential distribution 22 17 5\n", "2 beta distribution 22 15 7\n", "3 gamma distribution 20 16 4\n", "4 pearson distribution 19 4 15" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_degree = (\n", " pd.concat(\n", " [\n", " pd.DataFrame(nx_graph.degree, columns=['node', 'degree']).set_index('node'),\n", " pd.DataFrame(nx_graph.in_degree, columns=['node', 'in_degree']).set_index(\n", " 'node'\n", " ),\n", " pd.DataFrame(nx_graph.out_degree, columns=['node', 'out_degree']).set_index(\n", " 'node'\n", " ),\n", " ],\n", " axis=1,\n", " )\n", " .sort_values('degree', ascending=False)\n", " .reset_index()\n", ")\n", "\n", "df_degree = df_degree[~df_degree['node'].isin(DISTRIBUTION_BLACKLIST)]\n", "\n", "df_degree.head()" ] }, { "cell_type": "code", "execution_count": 10, "id": "coordinate-technician", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 0, 'Node degree')]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = sns.histplot(data=df_degree, x='degree')\n", "ax.set(xlabel='Node degree')" ] }, { "cell_type": "markdown", "id": "middle-convertible", "metadata": { "tags": [] }, "source": [ "We can observe that most distributions are related to less than $10$ other distributions and that there is one especially strong hub.\n", "This hub is the good old normal distribution.\n", "\n", "It is furthermore interesting to differentiate between high in- and high out-degrees, corresponding to distributions which are mentioned by many other and distributions which themselves mention many other distributions respectively." ] }, { "cell_type": "code", "execution_count": 11, "id": "biblical-noise", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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nodedegreein_degreeout_degree
0normal distribution53494
1exponential distribution22175
3gamma distribution20164
2beta distribution22157
6multivariate normal distribution15141
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" ], "text/plain": [ " node degree in_degree out_degree\n", "0 normal distribution 53 49 4\n", "1 exponential distribution 22 17 5\n", "3 gamma distribution 20 16 4\n", "2 beta distribution 22 15 7\n", "6 multivariate normal distribution 15 14 1" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# distributions which are mentioned by many others\n", "df_degree.sort_values('in_degree', ascending=False).head()" ] }, { "cell_type": "code", "execution_count": 12, "id": "genetic-easter", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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nodedegreein_degreeout_degree
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4pearson distribution19415
7metalog distribution14212
11compound poisson distribution12210
17beta-binomial distribution918
\n", "
" ], "text/plain": [ " node degree in_degree out_degree\n", "5 generalized normal distribution 16 0 16\n", "4 pearson distribution 19 4 15\n", "7 metalog distribution 14 2 12\n", "11 compound poisson distribution 12 2 10\n", "17 beta-binomial distribution 9 1 8" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# distributions which mention many others\n", "df_degree.sort_values('out_degree', ascending=False).head()" ] }, { "cell_type": "markdown", "id": "indie-breeding", "metadata": { "tags": [] }, "source": [ "## Plotting the distribution network\n", "\n", "As the whole distribution network is quite large ($233$ nodes and $460$ edges) we will look at various subsets of it.\n", "You can see the whole network at the end of the post." ] }, { "cell_type": "code", "execution_count": 13, "id": "quiet-console", "metadata": { "tags": [] }, "outputs": [], "source": [ "def plot_network(node_selection, **graph_attr):\n", " graph = graphviz.Digraph(\n", " engine='dot', graph_attr=dict(ratio=str(9 / 16), **graph_attr)\n", " )\n", "\n", " # do not forget possibly isolated nodes\n", " for node in node_selection:\n", " graph.node(node)\n", "\n", " # add edges\n", " for source, target_list in distribution_linkages.items():\n", " if source not in node_selection:\n", " continue\n", "\n", " for target in target_list:\n", " if target not in node_selection:\n", " continue\n", "\n", " graph.edge(source, target)\n", "\n", " return graph" ] }, { "cell_type": "markdown", "id": "manufactured-williams", "metadata": { "tags": [] }, "source": [ "Including only nodes with degrees higher than $10$ yields a clear view of the most common distributions and how they relate to each other." ] }, { "cell_type": "code", "execution_count": 14, "id": "annoying-tokyo", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "normal distribution\n", "\n", "normal distribution\n", "\n", "\n", "\n", "cauchy distribution\n", "\n", "cauchy distribution\n", "\n", "\n", "\n", "normal distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "exponential distribution\n", "\n", "exponential distribution\n", "\n", "\n", "\n", "exponential distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "gamma distribution\n", "\n", "gamma distribution\n", "\n", "\n", "\n", "exponential distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "poisson distribution\n", "\n", "poisson distribution\n", "\n", "\n", "\n", "exponential distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "beta distribution\n", "\n", "beta distribution\n", "\n", "\n", "\n", "gamma distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution\n", "\n", "pearson distribution\n", "\n", "\n", "\n", "pearson distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution\n", "\n", "metalog distribution\n", "\n", "\n", "\n", "pearson distribution->metalog distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized normal distribution\n", "\n", "generalized normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized normal distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate normal distribution\n", "\n", "multivariate normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "weibull distribution\n", "\n", "weibull distribution\n", "\n", "\n", "\n", "generalized normal distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "laplace distribution\n", "\n", "laplace distribution\n", "\n", "\n", "\n", "generalized normal distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->pearson distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "cauchy distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution\n", "\n", "compound poisson distribution\n", "\n", "\n", "\n", "compound poisson distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "laplace distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "node_selection = df_degree.loc[df_degree['degree'] > 10, 'node'].tolist()\n", "plot_network(node_selection, size='10')" ] }, { "cell_type": "markdown", "id": "handy-lingerie", "metadata": { "tags": [] }, "source": [ "Lowering the degree threshold to $5$ reveals the more complicated nature of the distribution landscape." ] }, { "cell_type": "code", "execution_count": 15, "id": "going-level", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "normal distribution\n", "\n", "normal distribution\n", "\n", "\n", "\n", "cauchy distribution\n", "\n", "cauchy distribution\n", "\n", "\n", "\n", "normal distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "student's t-distribution\n", "\n", "student's t-distribution\n", "\n", "\n", "\n", "normal distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "logistic distribution\n", "\n", "logistic distribution\n", "\n", "\n", "\n", "normal distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "exponential distribution\n", "\n", "exponential distribution\n", "\n", "\n", "\n", "exponential distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "gamma distribution\n", "\n", "gamma distribution\n", "\n", "\n", "\n", "exponential distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "poisson distribution\n", "\n", "poisson distribution\n", "\n", "\n", "\n", "exponential distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "binomial distribution\n", "\n", "binomial distribution\n", "\n", "\n", "\n", "exponential distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "geometric distribution\n", "\n", "geometric distribution\n", "\n", "\n", "\n", "exponential distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "beta distribution\n", "\n", "beta distribution\n", "\n", "\n", "\n", "dirichlet distribution\n", "\n", "dirichlet distribution\n", "\n", "\n", "\n", "beta distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "beta distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "negative binomial distribution\n", "\n", "negative binomial distribution\n", "\n", "\n", "\n", "beta distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "bernoulli distribution\n", "\n", "bernoulli distribution\n", "\n", "\n", "\n", "beta distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "gamma distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution\n", "\n", "pearson distribution\n", "\n", "\n", "\n", "pearson distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution\n", "\n", "metalog distribution\n", "\n", "\n", "\n", "pearson distribution->metalog distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "chi-squared distribution\n", "\n", "chi-squared distribution\n", "\n", "\n", "\n", "pearson distribution->chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution\n", "\n", "quantile-parameterized distribution\n", "\n", "\n", "\n", "pearson distribution->quantile-parameterized distribution\n", "\n", "\n", "\n", "\n", "\n", "hypergeometric distribution\n", "\n", "hypergeometric distribution\n", "\n", "\n", "\n", "pearson distribution->hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-gamma distribution\n", "\n", "inverse-gamma distribution\n", "\n", "\n", "\n", "pearson distribution->inverse-gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized normal distribution\n", "\n", "generalized normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized normal distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate normal distribution\n", "\n", "multivariate normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "weibull distribution\n", "\n", "weibull distribution\n", "\n", "\n", "\n", "generalized normal distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "laplace distribution\n", "\n", "laplace distribution\n", "\n", "\n", "\n", "generalized normal distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "log-normal distribution\n", "\n", "log-normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->pearson distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->quantile-parameterized distribution\n", "\n", "\n", "\n", "\n", "\n", "cauchy distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "stable distribution\n", "\n", "stable distribution\n", "\n", "\n", "\n", "cauchy distribution->stable distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution\n", "\n", "compound poisson distribution\n", "\n", "\n", "\n", "compound poisson distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution\n", "\n", "tweedie distribution\n", "\n", "\n", "\n", "compound poisson distribution->tweedie distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "laplace distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution\n", "\n", "gumbel distribution\n", "\n", "\n", "\n", "laplace distribution->gumbel distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "multinomial distribution\n", "\n", "multinomial distribution\n", "\n", "\n", "\n", "dirichlet distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "mixture distribution\n", "\n", "mixture distribution\n", "\n", "\n", "\n", "mixture distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "mixture distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "mixture distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution\n", "\n", "beta-binomial distribution\n", "\n", "\n", "\n", "beta-binomial distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution\n", "\n", "dirichlet-multinomial distribution\n", "\n", "\n", "\n", "beta-binomial distribution->dirichlet-multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->compound poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "multinomial distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "multinomial distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "negative binomial distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "asymmetric laplace distribution\n", "\n", "asymmetric laplace distribution\n", "\n", "\n", "\n", "asymmetric laplace distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "asymmetric laplace distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "student's t-distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "logistic distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->beta-binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "chi-squared distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "stable distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "stable distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "bernoulli distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix t-distribution\n", "\n", "matrix t-distribution\n", "\n", "\n", "\n", "matrix t-distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "log-normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->pearson distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->metalog distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "chi distribution\n", "\n", "chi distribution\n", "\n", "\n", "\n", "chi distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "chi distribution->chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "log-logistic distribution\n", "\n", "log-logistic distribution\n", "\n", "\n", "\n", "log-logistic distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "log-logistic distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix gamma distribution\n", "\n", "matrix gamma distribution\n", "\n", "\n", "\n", "matrix gamma distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix gamma distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped distribution\n", "\n", "wrapped distribution\n", "\n", "\n", "\n", "hypergeometric distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "trapezoidal distribution\n", "\n", "trapezoidal distribution\n", "\n", "\n", "\n", "trapezoidal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "trapezoidal distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse matrix gamma distribution\n", "\n", "inverse matrix gamma distribution\n", "\n", "\n", "\n", "inverse matrix gamma distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-gamma distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-gamma distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "von mises distribution\n", "\n", "von mises distribution\n", "\n", "\n", "\n", "von mises distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "node_selection = df_degree.loc[df_degree['degree'] > 5, 'node'].tolist()\n", "plot_network(node_selection, size='15')" ] }, { "cell_type": "markdown", "id": "otherwise-noise", "metadata": { "tags": [] }, "source": [ "Finally, removing the degree threshold let's us admire the unvarnished beauty of the universe in its entirety..." ] }, { "cell_type": "code", "execution_count": 16, "id": "impressive-workplace", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "normal distribution\n", "\n", "normal distribution\n", "\n", "\n", "\n", "cauchy distribution\n", "\n", "cauchy distribution\n", "\n", "\n", "\n", "normal distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "student's t-distribution\n", "\n", "student's t-distribution\n", "\n", "\n", "\n", "normal distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "logistic distribution\n", "\n", "logistic distribution\n", "\n", "\n", "\n", "normal distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "convergence in distribution\n", "\n", "convergence in distribution\n", "\n", "\n", "\n", "normal distribution->convergence in distribution\n", "\n", "\n", "\n", "\n", "\n", "exponential distribution\n", "\n", "exponential distribution\n", "\n", "\n", "\n", "exponential distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "gamma distribution\n", "\n", "gamma distribution\n", "\n", "\n", "\n", "exponential distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "poisson distribution\n", "\n", "poisson distribution\n", "\n", "\n", "\n", "exponential distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "binomial distribution\n", "\n", "binomial distribution\n", "\n", "\n", "\n", "exponential distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "geometric distribution\n", "\n", "geometric distribution\n", "\n", "\n", "\n", "exponential distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "beta distribution\n", "\n", "beta distribution\n", "\n", "\n", "\n", "dirichlet distribution\n", "\n", "dirichlet distribution\n", "\n", "\n", "\n", "beta distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "beta distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "negative binomial distribution\n", "\n", "negative binomial distribution\n", "\n", "\n", "\n", "beta distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "bernoulli distribution\n", "\n", "bernoulli distribution\n", "\n", "\n", "\n", "beta distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "beta prime distribution\n", "\n", "beta prime distribution\n", "\n", "\n", "\n", "beta distribution->beta prime distribution\n", "\n", "\n", "\n", "\n", "\n", "conjugate prior distribution\n", "\n", "conjugate prior distribution\n", "\n", "\n", "\n", "beta distribution->conjugate prior distribution\n", "\n", "\n", "\n", "\n", "\n", "gamma distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "erlang distribution\n", "\n", "erlang distribution\n", "\n", "\n", "\n", "gamma distribution->erlang distribution\n", "\n", "\n", "\n", "\n", "\n", "maximum entropy probability distribution\n", "\n", "maximum entropy probability distribution\n", "\n", "\n", "\n", "gamma distribution->maximum entropy probability distribution\n", "\n", "\n", "\n", "\n", "\n", "chi-square distribution\n", "\n", "chi-square distribution\n", "\n", "\n", "\n", "gamma distribution->chi-square distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution\n", "\n", "pearson distribution\n", "\n", "\n", "\n", "pearson distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution\n", "\n", "metalog distribution\n", "\n", "\n", "\n", "pearson distribution->metalog distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "chi-squared distribution\n", "\n", "chi-squared distribution\n", "\n", "\n", "\n", "pearson distribution->chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution\n", "\n", "quantile-parameterized distribution\n", "\n", "\n", "\n", "pearson distribution->quantile-parameterized distribution\n", "\n", "\n", "\n", "\n", "\n", "hypergeometric distribution\n", "\n", "hypergeometric distribution\n", "\n", "\n", "\n", "pearson distribution->hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-gamma distribution\n", "\n", "inverse-gamma distribution\n", "\n", "\n", "\n", "pearson distribution->inverse-gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "pearson distribution->beta prime distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized gamma distribution\n", "\n", "generalized gamma distribution\n", "\n", "\n", "\n", "pearson distribution->generalized gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "f-distribution\n", "\n", "f-distribution\n", "\n", "\n", "\n", "pearson distribution->f-distribution\n", "\n", "\n", "\n", "\n", "\n", "posterior distribution\n", "\n", "posterior distribution\n", "\n", "\n", "\n", "pearson distribution->posterior distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized normal distribution\n", "\n", "generalized normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized normal distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate normal distribution\n", "\n", "multivariate normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "weibull distribution\n", "\n", "weibull distribution\n", "\n", "\n", "\n", "generalized normal distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "laplace distribution\n", "\n", "laplace distribution\n", "\n", "\n", "\n", "generalized normal distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "log-normal distribution\n", "\n", "log-normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "bates distribution\n", "\n", "bates distribution\n", "\n", "\n", "\n", "generalized normal distribution->bates distribution\n", "\n", "\n", "\n", "\n", "\n", "irwin–hall distribution\n", "\n", "irwin–hall distribution\n", "\n", "\n", "\n", "generalized normal distribution->irwin–hall distribution\n", "\n", "\n", "\n", "\n", "\n", "symmetric distribution\n", "\n", "symmetric distribution\n", "\n", "\n", "\n", "generalized normal distribution->symmetric distribution\n", "\n", "\n", "\n", "\n", "\n", "continuous uniform distribution\n", "\n", "continuous uniform distribution\n", "\n", "\n", "\n", "generalized normal distribution->continuous uniform distribution\n", "\n", "\n", "\n", "\n", "\n", "folded normal distribution\n", "\n", "folded normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->folded normal distribution\n", "\n", "\n", "\n", "\n", "\n", "skew normal distribution\n", "\n", "skew normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->skew normal distribution\n", "\n", "\n", "\n", "\n", "\n", "infinitely divisible distribution\n", "\n", "infinitely divisible distribution\n", "\n", "\n", "\n", "generalized normal distribution->infinitely divisible distribution\n", "\n", "\n", "\n", "\n", "\n", "student t distribution\n", "\n", "student t distribution\n", "\n", "\n", "\n", "generalized normal distribution->student t distribution\n", "\n", "\n", "\n", "\n", "\n", "lognormal distribution\n", "\n", "lognormal distribution\n", "\n", "\n", "\n", "generalized normal distribution->lognormal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse normal distribution\n", "\n", "inverse normal distribution\n", "\n", "\n", "\n", "generalized normal distribution->inverse normal distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->pearson distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->quantile-parameterized distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->continuous uniform distribution\n", "\n", "\n", "\n", "\n", "\n", "metalog distribution->chi-square distribution\n", "\n", "\n", "\n", "\n", "\n", "student t-distribution\n", "\n", "student t-distribution\n", "\n", "\n", "\n", "metalog distribution->student t-distribution\n", "\n", "\n", "\n", "\n", "\n", "f distribution\n", "\n", "f distribution\n", "\n", "\n", "\n", "metalog distribution->f distribution\n", "\n", "\n", "\n", "\n", "\n", "cauchy distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "stable distribution\n", "\n", "stable distribution\n", "\n", "\n", "\n", "cauchy distribution->stable distribution\n", "\n", "\n", "\n", "\n", "\n", "lévy distribution\n", "\n", "lévy distribution\n", "\n", "\n", "\n", "cauchy distribution->lévy distribution\n", "\n", "\n", "\n", "\n", "\n", "ratio distribution\n", "\n", "ratio distribution\n", "\n", "\n", "\n", "cauchy distribution->ratio distribution\n", "\n", "\n", "\n", "\n", "\n", "particle-size distribution\n", "\n", "particle-size distribution\n", "\n", "\n", "\n", "weibull distribution->particle-size distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution\n", "\n", "compound poisson distribution\n", "\n", "\n", "\n", "compound poisson distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution\n", "\n", "tweedie distribution\n", "\n", "\n", "\n", "compound poisson distribution->tweedie distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "compound poisson distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "continuous distribution\n", "\n", "continuous distribution\n", "\n", "\n", "\n", "compound poisson distribution->continuous distribution\n", "\n", "\n", "\n", "\n", "\n", "discrete distribution\n", "\n", "discrete distribution\n", "\n", "\n", "\n", "compound poisson distribution->discrete distribution\n", "\n", "\n", "\n", "\n", "\n", "hermite distribution\n", "\n", "hermite distribution\n", "\n", "\n", "\n", "compound poisson distribution->hermite distribution\n", "\n", "\n", "\n", "\n", "\n", "geometric poisson distribution\n", "\n", "geometric poisson distribution\n", "\n", "\n", "\n", "compound poisson distribution->geometric poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "laplace distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution\n", "\n", "gumbel distribution\n", "\n", "\n", "\n", "laplace distribution->gumbel distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "gumbel distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized extreme value distribution\n", "\n", "generalized extreme value distribution\n", "\n", "\n", "\n", "gumbel distribution->generalized extreme value distribution\n", "\n", "\n", "\n", "\n", "\n", "gompertz distribution\n", "\n", "gompertz distribution\n", "\n", "\n", "\n", "gumbel distribution->gompertz distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "multinomial distribution\n", "\n", "multinomial distribution\n", "\n", "\n", "\n", "dirichlet distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "categorical distribution\n", "\n", "categorical distribution\n", "\n", "\n", "\n", "dirichlet distribution->categorical distribution\n", "\n", "\n", "\n", "\n", "\n", "prior distribution\n", "\n", "prior distribution\n", "\n", "\n", "\n", "dirichlet distribution->prior distribution\n", "\n", "\n", "\n", "\n", "\n", "mixture distribution\n", "\n", "mixture distribution\n", "\n", "\n", "\n", "mixture distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "mixture distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "mixture distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate distribution\n", "\n", "multivariate distribution\n", "\n", "\n", "\n", "mixture distribution->multivariate distribution\n", "\n", "\n", "\n", "\n", "\n", "compound probability distribution\n", "\n", "compound probability distribution\n", "\n", "\n", "\n", "mixture distribution->compound probability distribution\n", "\n", "\n", "\n", "\n", "\n", "mixture distribution->discrete distribution\n", "\n", "\n", "\n", "\n", "\n", "multimodal distribution\n", "\n", "multimodal distribution\n", "\n", "\n", "\n", "mixture distribution->multimodal distribution\n", "\n", "\n", "\n", "\n", "\n", "bimodal distribution\n", "\n", "bimodal distribution\n", "\n", "\n", "\n", "mixture distribution->bimodal distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution\n", "\n", "beta-binomial distribution\n", "\n", "\n", "\n", "beta-binomial distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution\n", "\n", "dirichlet-multinomial distribution\n", "\n", "\n", "\n", "beta-binomial distribution->dirichlet-multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta-binomial distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "discrete uniform distribution\n", "\n", "discrete uniform distribution\n", "\n", "\n", "\n", "beta-binomial distribution->discrete uniform distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->compound poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "tweedie distribution->convergence in distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse gaussian distribution\n", "\n", "inverse gaussian distribution\n", "\n", "\n", "\n", "tweedie distribution->inverse gaussian distribution\n", "\n", "\n", "\n", "\n", "\n", "wigner semicircle distribution\n", "\n", "wigner semicircle distribution\n", "\n", "\n", "\n", "tweedie distribution->wigner semicircle distribution\n", "\n", "\n", "\n", "\n", "\n", "multinomial distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "multinomial distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "multinomial distribution->categorical distribution\n", "\n", "\n", "\n", "\n", "\n", "negative binomial distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "asymmetric laplace distribution\n", "\n", "asymmetric laplace distribution\n", "\n", "\n", "\n", "asymmetric laplace distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "asymmetric laplace distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "student's t-distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalised hyperbolic distribution\n", "\n", "generalised hyperbolic distribution\n", "\n", "\n", "\n", "student's t-distribution->generalised hyperbolic distribution\n", "\n", "\n", "\n", "\n", "\n", "logistic distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "tukey lambda distribution\n", "\n", "tukey lambda distribution\n", "\n", "\n", "\n", "logistic distribution->tukey lambda distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->beta-binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->categorical distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet-multinomial distribution->compound probability distribution\n", "\n", "\n", "\n", "\n", "\n", "chi-squared distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral chi-square distribution\n", "\n", "noncentral chi-square distribution\n", "\n", "\n", "\n", "chi-squared distribution->noncentral chi-square distribution\n", "\n", "\n", "\n", "\n", "\n", "stable distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "stable distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "bernoulli distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix t-distribution\n", "\n", "matrix t-distribution\n", "\n", "\n", "\n", "matrix t-distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate t-distribution\n", "\n", "multivariate t-distribution\n", "\n", "\n", "\n", "matrix t-distribution->multivariate t-distribution\n", "\n", "\n", "\n", "\n", "\n", "compound distribution\n", "\n", "compound distribution\n", "\n", "\n", "\n", "matrix t-distribution->compound distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix normal distribution\n", "\n", "matrix normal distribution\n", "\n", "\n", "\n", "matrix t-distribution->matrix normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse wishart distribution\n", "\n", "inverse wishart distribution\n", "\n", "\n", "\n", "matrix t-distribution->inverse wishart distribution\n", "\n", "\n", "\n", "\n", "\n", "posterior predictive distribution\n", "\n", "posterior predictive distribution\n", "\n", "\n", "\n", "matrix t-distribution->posterior predictive distribution\n", "\n", "\n", "\n", "\n", "\n", "log-normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "log-normal distribution->maximum entropy probability distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->pearson distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->metalog distribution\n", "\n", "\n", "\n", "\n", "\n", "quantile-parameterized distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "chi distribution\n", "\n", "chi distribution\n", "\n", "\n", "\n", "chi distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "chi distribution->chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "maxwell–boltzmann distribution\n", "\n", "maxwell–boltzmann distribution\n", "\n", "\n", "\n", "chi distribution->maxwell–boltzmann distribution\n", "\n", "\n", "\n", "\n", "\n", "rayleigh distribution\n", "\n", "rayleigh distribution\n", "\n", "\n", "\n", "chi distribution->rayleigh distribution\n", "\n", "\n", "\n", "\n", "\n", "log-logistic distribution\n", "\n", "log-logistic distribution\n", "\n", "\n", "\n", "log-logistic distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "log-logistic distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "income distribution\n", "\n", "income distribution\n", "\n", "\n", "\n", "log-logistic distribution->income distribution\n", "\n", "\n", "\n", "\n", "\n", "heavy-tailed distribution\n", "\n", "heavy-tailed distribution\n", "\n", "\n", "\n", "log-logistic distribution->heavy-tailed distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix gamma distribution\n", "\n", "matrix gamma distribution\n", "\n", "\n", "\n", "matrix gamma distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix gamma distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix gamma distribution->compound distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix gamma distribution->matrix normal distribution\n", "\n", "\n", "\n", "\n", "\n", "wishart distribution\n", "\n", "wishart distribution\n", "\n", "\n", "\n", "matrix gamma distribution->wishart distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized matrix t-distribution\n", "\n", "generalized matrix t-distribution\n", "\n", "\n", "\n", "matrix gamma distribution->generalized matrix t-distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped distribution\n", "\n", "wrapped distribution\n", "\n", "\n", "\n", "hypergeometric distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "trapezoidal distribution\n", "\n", "trapezoidal distribution\n", "\n", "\n", "\n", "trapezoidal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "trapezoidal distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "trapezoidal distribution->bates distribution\n", "\n", "\n", "\n", "\n", "\n", "trapezoidal distribution->irwin–hall distribution\n", "\n", "\n", "\n", "\n", "\n", "trapezoidal distribution->multimodal distribution\n", "\n", "\n", "\n", "\n", "\n", "triangular distribution\n", "\n", "triangular distribution\n", "\n", "\n", "\n", "trapezoidal distribution->triangular distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse matrix gamma distribution\n", "\n", "inverse matrix gamma distribution\n", "\n", "\n", "\n", "inverse matrix gamma distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse matrix gamma distribution->compound distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse matrix gamma distribution->matrix normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse matrix gamma distribution->generalized matrix t-distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse matrix gamma distribution->inverse wishart distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse gamma distribution\n", "\n", "inverse gamma distribution\n", "\n", "\n", "\n", "inverse matrix gamma distribution->inverse gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-gamma distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-gamma distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "scaled inverse chi-squared distribution\n", "\n", "scaled inverse chi-squared distribution\n", "\n", "\n", "\n", "inverse-gamma distribution->scaled inverse chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "von mises distribution\n", "\n", "von mises distribution\n", "\n", "\n", "\n", "von mises distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "von mises–fisher distribution\n", "\n", "von mises–fisher distribution\n", "\n", "\n", "\n", "von mises distribution->von mises–fisher distribution\n", "\n", "\n", "\n", "\n", "\n", "von mises distribution->maximum entropy probability distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped normal distribution\n", "\n", "wrapped normal distribution\n", "\n", "\n", "\n", "von mises distribution->wrapped normal distribution\n", "\n", "\n", "\n", "\n", "\n", "rectified gaussian distribution\n", "\n", "rectified gaussian distribution\n", "\n", "\n", "\n", "rectified gaussian distribution->continuous distribution\n", "\n", "\n", "\n", "\n", "\n", "rectified gaussian distribution->discrete distribution\n", "\n", "\n", "\n", "\n", "\n", "standard normal distribution\n", "\n", "standard normal distribution\n", "\n", "\n", "\n", "rectified gaussian distribution->standard normal distribution\n", "\n", "\n", "\n", "\n", "\n", "truncated gaussian distribution\n", "\n", "truncated gaussian distribution\n", "\n", "\n", "\n", "rectified gaussian distribution->truncated gaussian distribution\n", "\n", "\n", "\n", "\n", "\n", "gaussian distribution\n", "\n", "gaussian distribution\n", "\n", "\n", "\n", "rectified gaussian distribution->gaussian distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral f-distribution\n", "\n", "noncentral f-distribution\n", "\n", "\n", "\n", "noncentral f-distribution->chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral chi-squared distribution\n", "\n", "noncentral chi-squared distribution\n", "\n", "\n", "\n", "noncentral f-distribution->noncentral chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral f-distribution->f-distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral distribution\n", "\n", "noncentral distribution\n", "\n", "\n", "\n", "noncentral f-distribution->noncentral distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral t-distribution\n", "\n", "noncentral t-distribution\n", "\n", "\n", "\n", "noncentral f-distribution->noncentral t-distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate t-distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate t-distribution->matrix t-distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate probability distribution\n", "\n", "multivariate probability distribution\n", "\n", "\n", "\n", "multivariate t-distribution->multivariate probability distribution\n", "\n", "\n", "\n", "\n", "\n", "erlang distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "erlang distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "fisher's noncentral hypergeometric distribution\n", "\n", "fisher's noncentral hypergeometric distribution\n", "\n", "\n", "\n", "fisher's noncentral hypergeometric distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "fisher's noncentral hypergeometric distribution->hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "conditional probability distribution\n", "\n", "conditional probability distribution\n", "\n", "\n", "\n", "fisher's noncentral hypergeometric distribution->conditional probability distribution\n", "\n", "\n", "\n", "\n", "\n", "wallenius' noncentral hypergeometric distribution\n", "\n", "wallenius' noncentral hypergeometric distribution\n", "\n", "\n", "\n", "fisher's noncentral hypergeometric distribution->wallenius' noncentral hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "fréchet distribution\n", "\n", "fréchet distribution\n", "\n", "\n", "\n", "fréchet distribution->generalized extreme value distribution\n", "\n", "\n", "\n", "\n", "\n", "fisher–tippett distribution\n", "\n", "fisher–tippett distribution\n", "\n", "\n", "\n", "fréchet distribution->fisher–tippett distribution\n", "\n", "\n", "\n", "\n", "\n", "bates distribution->irwin–hall distribution\n", "\n", "\n", "\n", "\n", "\n", "bates distribution->continuous uniform distribution\n", "\n", "\n", "\n", "\n", "\n", "hypoexponential distribution\n", "\n", "hypoexponential distribution\n", "\n", "\n", "\n", "hypoexponential distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "hypoexponential distribution->erlang distribution\n", "\n", "\n", "\n", "\n", "\n", "hypoexponential distribution->continuous distribution\n", "\n", "\n", "\n", "\n", "\n", "hyper-exponential distribution\n", "\n", "hyper-exponential distribution\n", "\n", "\n", "\n", "hypoexponential distribution->hyper-exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "irwin–hall distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "irwin–hall distribution->bates distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized extreme value distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized extreme value distribution->gumbel distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized extreme value distribution->fréchet distribution\n", "\n", "\n", "\n", "\n", "\n", "burr distribution\n", "\n", "burr distribution\n", "\n", "\n", "\n", "burr distribution->log-logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "champernowne distribution\n", "\n", "champernowne distribution\n", "\n", "\n", "\n", "burr distribution->champernowne distribution\n", "\n", "\n", "\n", "\n", "\n", "pareto distribution\n", "\n", "pareto distribution\n", "\n", "\n", "\n", "burr distribution->pareto distribution\n", "\n", "\n", "\n", "\n", "\n", "fisk distribution\n", "\n", "fisk distribution\n", "\n", "\n", "\n", "burr distribution->fisk distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-chi-squared distribution\n", "\n", "inverse-chi-squared distribution\n", "\n", "\n", "\n", "inverse-chi-squared distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-chi-squared distribution->chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-chi-squared distribution->prior distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-chi-squared distribution->posterior distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized inverse gaussian distribution\n", "\n", "generalized inverse gaussian distribution\n", "\n", "\n", "\n", "generalised hyperbolic distribution->generalized inverse gaussian distribution\n", "\n", "\n", "\n", "\n", "\n", "beta prime distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "beta prime distribution->pearson distribution\n", "\n", "\n", "\n", "\n", "\n", "beta prime distribution->conjugate prior distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized multivariate log-gamma distribution\n", "\n", "generalized multivariate log-gamma distribution\n", "\n", "\n", "\n", "generalized multivariate log-gamma distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized multivariate log-gamma distribution->gumbel distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized multivariate log-gamma distribution->multivariate distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized multivariate log-gamma distribution->prior distribution\n", "\n", "\n", "\n", "\n", "\n", "type i extreme value distribution\n", "\n", "type i extreme value distribution\n", "\n", "\n", "\n", "generalized multivariate log-gamma distribution->type i extreme value distribution\n", "\n", "\n", "\n", "\n", "\n", "scaled inverse chi-squared distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "scaled inverse chi-squared distribution->inverse-gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "scaled inverse chi-squared distribution->inverse-chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "scaled inverse chi-squared distribution->maximum entropy probability distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral chi-squared distribution->noncentral distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral chi-squared distribution->chi-square distribution\n", "\n", "\n", "\n", "\n", "\n", "lévy distribution->stable distribution\n", "\n", "\n", "\n", "\n", "\n", "lévy distribution->inverse-gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "categorical distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "categorical distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "hyperexponential distribution\n", "\n", "hyperexponential distribution\n", "\n", "\n", "\n", "hyperexponential distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "hyperexponential distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "hyperexponential distribution->hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "hyperexponential distribution->hypoexponential distribution\n", "\n", "\n", "\n", "\n", "\n", "hyperexponential distribution->heavy-tailed distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized gamma distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized gamma distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized gamma distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "half-normal distribution\n", "\n", "half-normal distribution\n", "\n", "\n", "\n", "generalized gamma distribution->half-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized chi-squared distribution\n", "\n", "generalized chi-squared distribution\n", "\n", "\n", "\n", "generalized chi-squared distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized chi-squared distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized chi-squared distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized chi-squared distribution->noncentral chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "variance-gamma distribution\n", "\n", "variance-gamma distribution\n", "\n", "\n", "\n", "variance-gamma distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "variance-gamma distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "variance-gamma distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "variance-gamma distribution->generalised hyperbolic distribution\n", "\n", "\n", "\n", "\n", "\n", "elliptical distribution\n", "\n", "elliptical distribution\n", "\n", "\n", "\n", "elliptical distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "elliptical distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "elliptical distribution->multivariate t-distribution\n", "\n", "\n", "\n", "\n", "\n", "elliptical distribution->symmetric distribution\n", "\n", "\n", "\n", "\n", "\n", "shape of the distribution\n", "\n", "shape of the distribution\n", "\n", "\n", "\n", "shape of the distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "shape of the distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "shape of the distribution->pareto distribution\n", "\n", "\n", "\n", "\n", "\n", "shape of the distribution->bimodal distribution\n", "\n", "\n", "\n", "\n", "\n", "von mises–fisher distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "von mises–fisher distribution->von mises distribution\n", "\n", "\n", "\n", "\n", "\n", "logarithmic distribution\n", "\n", "logarithmic distribution\n", "\n", "\n", "\n", "logarithmic distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "logarithmic distribution->compound poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "logarithmic distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "null distribution\n", "\n", "null distribution\n", "\n", "\n", "\n", "f-distribution->null distribution\n", "\n", "\n", "\n", "\n", "\n", "fisher–tippett distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "fisher–tippett distribution->gumbel distribution\n", "\n", "\n", "\n", "\n", "\n", "fisher–tippett distribution->fréchet distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral beta distribution\n", "\n", "noncentral beta distribution\n", "\n", "\n", "\n", "noncentral beta distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral beta distribution->chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral beta distribution->noncentral chi-squared distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral beta distribution->noncentral distribution\n", "\n", "\n", "\n", "\n", "\n", "holtsmark distribution\n", "\n", "holtsmark distribution\n", "\n", "\n", "\n", "holtsmark distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "holtsmark distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "holtsmark distribution->stable distribution\n", "\n", "\n", "\n", "\n", "\n", "holtsmark distribution->lévy distribution\n", "\n", "\n", "\n", "\n", "\n", "phase-type distribution\n", "\n", "phase-type distribution\n", "\n", "\n", "\n", "phase-type distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "discrete phase-type distribution\n", "\n", "discrete phase-type distribution\n", "\n", "\n", "\n", "phase-type distribution->discrete phase-type distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix normal distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "sampling distribution\n", "\n", "sampling distribution\n", "\n", "\n", "\n", "sampling distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "joint probability distribution\n", "\n", "joint probability distribution\n", "\n", "\n", "\n", "sampling distribution->joint probability distribution\n", "\n", "\n", "\n", "\n", "\n", "asymptotic distribution\n", "\n", "asymptotic distribution\n", "\n", "\n", "\n", "sampling distribution->asymptotic distribution\n", "\n", "\n", "\n", "\n", "\n", "wishart distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "wishart distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped exponential distribution\n", "\n", "wrapped exponential distribution\n", "\n", "\n", "\n", "wrapped exponential distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped exponential distribution->wrapped distribution\n", "\n", "\n", "\n", "\n", "\n", "delaporte distribution\n", "\n", "delaporte distribution\n", "\n", "\n", "\n", "delaporte distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "delaporte distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "delaporte distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "delaporte distribution->compound distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped normal distribution->wrapped distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped normal distribution->von mises distribution\n", "\n", "\n", "\n", "\n", "\n", "champernowne distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "champernowne distribution->burr distribution\n", "\n", "\n", "\n", "\n", "\n", "champernowne distribution->fisk distribution\n", "\n", "\n", "\n", "\n", "\n", "maxwell–boltzmann distribution->chi distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate distribution->conditional probability distribution\n", "\n", "\n", "\n", "\n", "\n", "degenerate distribution\n", "\n", "degenerate distribution\n", "\n", "\n", "\n", "degenerate distribution->multivariate distribution\n", "\n", "\n", "\n", "\n", "\n", "degenerate distribution->symmetric distribution\n", "\n", "\n", "\n", "\n", "\n", "degenerate distribution->joint probability distribution\n", "\n", "\n", "\n", "\n", "\n", "univariate distribution\n", "\n", "univariate distribution\n", "\n", "\n", "\n", "degenerate distribution->univariate distribution\n", "\n", "\n", "\n", "\n", "\n", "rayleigh distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "rayleigh distribution->chi distribution\n", "\n", "\n", "\n", "\n", "\n", "beta negative binomial distribution\n", "\n", "beta negative binomial distribution\n", "\n", "\n", "\n", "beta negative binomial distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "beta negative binomial distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "beta negative binomial distribution->compound probability distribution\n", "\n", "\n", "\n", "\n", "\n", "tsallis distribution\n", "\n", "tsallis distribution\n", "\n", "\n", "\n", "half-normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "half-normal distribution->folded normal distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized logistic distribution\n", "\n", "generalized logistic distribution\n", "\n", "\n", "\n", "generalized logistic distribution->log-logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "shifted log-logistic distribution\n", "\n", "shifted log-logistic distribution\n", "\n", "\n", "\n", "generalized logistic distribution->shifted log-logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "q-gaussian distribution\n", "\n", "q-gaussian distribution\n", "\n", "\n", "\n", "q-gaussian distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "q-gaussian distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "q-gaussian distribution->tsallis distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse gaussian distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped asymmetric laplace distribution\n", "\n", "wrapped asymmetric laplace distribution\n", "\n", "\n", "\n", "wrapped asymmetric laplace distribution->asymmetric laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped asymmetric laplace distribution->wrapped distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped asymmetric laplace distribution->wrapped exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "slash distribution\n", "\n", "slash distribution\n", "\n", "\n", "\n", "slash distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "slash distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "slash distribution->ratio distribution\n", "\n", "\n", "\n", "\n", "\n", "kent distribution\n", "\n", "kent distribution\n", "\n", "\n", "\n", "kent distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "kent distribution->von mises–fisher distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized dirichlet distribution\n", "\n", "generalized dirichlet distribution\n", "\n", "\n", "\n", "generalized dirichlet distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized dirichlet distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "generalized dirichlet distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "geometric stable distribution\n", "\n", "geometric stable distribution\n", "\n", "\n", "\n", "geometric stable distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "geometric stable distribution->asymmetric laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "mittag-leffler distribution\n", "\n", "mittag-leffler distribution\n", "\n", "\n", "\n", "geometric stable distribution->mittag-leffler distribution\n", "\n", "\n", "\n", "\n", "\n", "hotelling's t-squared distribution\n", "\n", "hotelling's t-squared distribution\n", "\n", "\n", "\n", "hotelling's t-squared distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "hotelling's t-squared distribution->f-distribution\n", "\n", "\n", "\n", "\n", "\n", "hotelling's t-squared distribution->multivariate probability distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate laplace distribution\n", "\n", "multivariate laplace distribution\n", "\n", "\n", "\n", "multivariate laplace distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate laplace distribution->asymmetric laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "marginal distribution\n", "\n", "marginal distribution\n", "\n", "\n", "\n", "multivariate laplace distribution->marginal distribution\n", "\n", "\n", "\n", "\n", "\n", "discrete phase-type distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "discrete phase-type distribution->phase-type distribution\n", "\n", "\n", "\n", "\n", "\n", "wallenius' noncentral hypergeometric distribution->hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "wallenius' noncentral hypergeometric distribution->fisher's noncentral hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "negative multinomial distribution\n", "\n", "negative multinomial distribution\n", "\n", "\n", "\n", "negative multinomial distribution->multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "negative multinomial distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet negative multinomial distribution\n", "\n", "dirichlet negative multinomial distribution\n", "\n", "\n", "\n", "dirichlet negative multinomial distribution->dirichlet distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet negative multinomial distribution->beta negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "dirichlet negative multinomial distribution->negative multinomial distribution\n", "\n", "\n", "\n", "\n", "\n", "extended negative binomial distribution\n", "\n", "extended negative binomial distribution\n", "\n", "\n", "\n", "extended negative binomial distribution->negative binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "extended negative binomial distribution->logarithmic distribution\n", "\n", "\n", "\n", "\n", "\n", "truncated distribution\n", "\n", "truncated distribution\n", "\n", "\n", "\n", "extended negative binomial distribution->truncated distribution\n", "\n", "\n", "\n", "\n", "\n", "conditional distribution\n", "\n", "conditional distribution\n", "\n", "\n", "\n", "truncated distribution->conditional distribution\n", "\n", "\n", "\n", "\n", "\n", "q-weibull distribution\n", "\n", "q-weibull distribution\n", "\n", "\n", "\n", "q-weibull distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "q-weibull distribution->tsallis distribution\n", "\n", "\n", "\n", "\n", "\n", "lomax distribution\n", "\n", "lomax distribution\n", "\n", "\n", "\n", "q-weibull distribution->lomax distribution\n", "\n", "\n", "\n", "\n", "\n", "linnik distribution\n", "\n", "linnik distribution\n", "\n", "\n", "\n", "linnik distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "linnik distribution->asymmetric laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "linnik distribution->mittag-leffler distribution\n", "\n", "\n", "\n", "\n", "\n", "joint probability distribution->conditional probability distribution\n", "\n", "\n", "\n", "\n", "\n", "folded normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped laplace distribution\n", "\n", "wrapped laplace distribution\n", "\n", "\n", "\n", "wrapped laplace distribution->asymmetric laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped laplace distribution->wrapped distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped laplace distribution->wrapped exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "rayleigh mixture distribution\n", "\n", "rayleigh mixture distribution\n", "\n", "\n", "\n", "rayleigh mixture distribution->compound distribution\n", "\n", "\n", "\n", "\n", "\n", "rayleigh mixture distribution->sampling distribution\n", "\n", "\n", "\n", "\n", "\n", "rayleigh mixture distribution->rayleigh distribution\n", "\n", "\n", "\n", "\n", "\n", "conway–maxwell–poisson distribution\n", "\n", "conway–maxwell–poisson distribution\n", "\n", "\n", "\n", "conway–maxwell–poisson distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "conway–maxwell–poisson distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "conway–maxwell–poisson distribution->bernoulli distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral chi distribution\n", "\n", "noncentral chi distribution\n", "\n", "\n", "\n", "noncentral chi distribution->chi distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral chi distribution->noncentral distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate stable distribution\n", "\n", "multivariate stable distribution\n", "\n", "\n", "\n", "multivariate stable distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "multivariate stable distribution->stable distribution\n", "\n", "\n", "\n", "\n", "\n", "q-exponential distribution\n", "\n", "q-exponential distribution\n", "\n", "\n", "\n", "q-exponential distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "q-exponential distribution->tsallis distribution\n", "\n", "\n", "\n", "\n", "\n", "normal-inverse gaussian distribution\n", "\n", "normal-inverse gaussian distribution\n", "\n", "\n", "\n", "normal-inverse gaussian distribution->generalised hyperbolic distribution\n", "\n", "\n", "\n", "\n", "\n", "normal-inverse gaussian distribution->inverse gaussian distribution\n", "\n", "\n", "\n", "\n", "\n", "lomax distribution->pareto distribution\n", "\n", "\n", "\n", "\n", "\n", "log-laplace distribution\n", "\n", "log-laplace distribution\n", "\n", "\n", "\n", "log-laplace distribution->laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "log-laplace distribution->asymmetric laplace distribution\n", "\n", "\n", "\n", "\n", "\n", "lévy skew alpha-stable distribution\n", "\n", "lévy skew alpha-stable distribution\n", "\n", "\n", "\n", "lévy skew alpha-stable distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "lévy skew alpha-stable distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "relativistic breit–wigner distribution\n", "\n", "relativistic breit–wigner distribution\n", "\n", "\n", "\n", "relativistic breit–wigner distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "relativistic breit–wigner distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "arcsine distribution\n", "\n", "arcsine distribution\n", "\n", "\n", "\n", "arcsine distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "arcsine distribution->pearson distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped cauchy distribution\n", "\n", "wrapped cauchy distribution\n", "\n", "\n", "\n", "wrapped cauchy distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped cauchy distribution->wrapped distribution\n", "\n", "\n", "\n", "\n", "\n", "zero-truncated poisson distribution\n", "\n", "zero-truncated poisson distribution\n", "\n", "\n", "\n", "zero-truncated poisson distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "zero-truncated poisson distribution->truncated distribution\n", "\n", "\n", "\n", "\n", "\n", "singular distribution\n", "\n", "singular distribution\n", "\n", "\n", "\n", "cantor distribution\n", "\n", "cantor distribution\n", "\n", "\n", "\n", "singular distribution->cantor distribution\n", "\n", "\n", "\n", "\n", "\n", "cantor distribution->singular distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped lévy distribution\n", "\n", "wrapped lévy distribution\n", "\n", "\n", "\n", "wrapped lévy distribution->wrapped distribution\n", "\n", "\n", "\n", "\n", "\n", "wrapped lévy distribution->lévy distribution\n", "\n", "\n", "\n", "\n", "\n", "type-2 gumbel distribution\n", "\n", "type-2 gumbel distribution\n", "\n", "\n", "\n", "type-2 gumbel distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "type-2 gumbel distribution->fréchet distribution\n", "\n", "\n", "\n", "\n", "\n", "birnbaum–saunders distribution\n", "\n", "birnbaum–saunders distribution\n", "\n", "\n", "\n", "birnbaum–saunders distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "birnbaum–saunders distribution->standard normal distribution\n", "\n", "\n", "\n", "\n", "\n", "bingham distribution\n", "\n", "bingham distribution\n", "\n", "\n", "\n", "bingham distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "bingham distribution->kent distribution\n", "\n", "\n", "\n", "\n", "\n", "beta rectangular distribution\n", "\n", "beta rectangular distribution\n", "\n", "\n", "\n", "beta rectangular distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "beta rectangular distribution->mixture distribution\n", "\n", "\n", "\n", "\n", "\n", "discrete uniform distribution->symmetric distribution\n", "\n", "\n", "\n", "\n", "\n", "zeta distribution\n", "\n", "zeta distribution\n", "\n", "\n", "\n", "yule–simon distribution\n", "\n", "yule–simon distribution\n", "\n", "\n", "\n", "zeta distribution->yule–simon distribution\n", "\n", "\n", "\n", "\n", "\n", "zipf distribution\n", "\n", "zipf distribution\n", "\n", "\n", "\n", "zipf distribution->zeta distribution\n", "\n", "\n", "\n", "\n", "\n", "rank-frequency distribution\n", "\n", "rank-frequency distribution\n", "\n", "\n", "\n", "zipf distribution->rank-frequency distribution\n", "\n", "\n", "\n", "\n", "\n", "exponentially modified gaussian distribution\n", "\n", "exponentially modified gaussian distribution\n", "\n", "\n", "\n", "exponentially modified gaussian distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "exponentially modified gaussian distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "noncentral t-distribution->student's t-distribution\n", "\n", "\n", "\n", "\n", "\n", "gaussian minus exponential distribution\n", "\n", "gaussian minus exponential distribution\n", "\n", "\n", "\n", "gaussian minus exponential distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "gaussian minus exponential distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "wigner semicircle distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "hyperbolic distribution\n", "\n", "hyperbolic distribution\n", "\n", "\n", "\n", "hyperbolic distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "hyperbolic distribution->generalised hyperbolic distribution\n", "\n", "\n", "\n", "\n", "\n", "shifted log-logistic distribution->generalized logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "shifted gompertz distribution\n", "\n", "shifted gompertz distribution\n", "\n", "\n", "\n", "shifted gompertz distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "shifted gompertz distribution->gumbel distribution\n", "\n", "\n", "\n", "\n", "\n", "skew normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "bivariate normal distribution\n", "\n", "bivariate normal distribution\n", "\n", "\n", "\n", "normal-wishart distribution\n", "\n", "normal-wishart distribution\n", "\n", "\n", "\n", "normal-wishart distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "normal-gamma distribution\n", "\n", "normal-gamma distribution\n", "\n", "\n", "\n", "normal-gamma distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "normal-inverse-wishart distribution\n", "\n", "normal-inverse-wishart distribution\n", "\n", "\n", "\n", "normal-inverse-wishart distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "skellam distribution\n", "\n", "skellam distribution\n", "\n", "\n", "\n", "skellam distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "normal-inverse-gamma distribution\n", "\n", "normal-inverse-gamma distribution\n", "\n", "\n", "\n", "normal-inverse-gamma distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "pert distribution\n", "\n", "pert distribution\n", "\n", "\n", "\n", "pert distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "poisson binomial distribution\n", "\n", "poisson binomial distribution\n", "\n", "\n", "\n", "poisson binomial distribution->binomial distribution\n", "\n", "\n", "\n", "\n", "\n", "poly-weibull distribution\n", "\n", "poly-weibull distribution\n", "\n", "\n", "\n", "poly-weibull distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse distribution\n", "\n", "inverse distribution\n", "\n", "\n", "\n", "reciprocal distribution\n", "\n", "reciprocal distribution\n", "\n", "\n", "\n", "reciprocal distribution->inverse distribution\n", "\n", "\n", "\n", "\n", "\n", "rice distribution\n", "\n", "rice distribution\n", "\n", "\n", "\n", "rice distribution->bivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "negative hypergeometric distribution\n", "\n", "negative hypergeometric distribution\n", "\n", "\n", "\n", "negative hypergeometric distribution->hypergeometric distribution\n", "\n", "\n", "\n", "\n", "\n", "nakagami distribution\n", "\n", "nakagami distribution\n", "\n", "\n", "\n", "nakagami distribution->gamma distribution\n", "\n", "\n", "\n", "\n", "\n", "gaussian q-distribution\n", "\n", "gaussian q-distribution\n", "\n", "\n", "\n", "gaussian q-distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "flory–schulz distribution\n", "\n", "flory–schulz distribution\n", "\n", "\n", "\n", "flory–schulz distribution->geometric distribution\n", "\n", "\n", "\n", "\n", "\n", "displaced poisson distribution\n", "\n", "displaced poisson distribution\n", "\n", "\n", "\n", "displaced poisson distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "discrete weibull distribution\n", "\n", "discrete weibull distribution\n", "\n", "\n", "\n", "discrete weibull distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "dagum distribution\n", "\n", "dagum distribution\n", "\n", "\n", "\n", "dagum distribution->income distribution\n", "\n", "\n", "\n", "\n", "\n", "borel distribution\n", "\n", "borel distribution\n", "\n", "\n", "\n", "borel distribution->poisson distribution\n", "\n", "\n", "\n", "\n", "\n", "boltzmann distribution\n", "\n", "boltzmann distribution\n", "\n", "\n", "\n", "boltzmann distribution->maxwell–boltzmann distribution\n", "\n", "\n", "\n", "\n", "\n", "bivariate von mises distribution\n", "\n", "bivariate von mises distribution\n", "\n", "\n", "\n", "bivariate von mises distribution->multivariate normal distribution\n", "\n", "\n", "\n", "\n", "\n", "benktander type i distribution\n", "\n", "benktander type i distribution\n", "\n", "\n", "\n", "benktander type i distribution->log-normal distribution\n", "\n", "\n", "\n", "\n", "\n", "benktander type ii distribution\n", "\n", "benktander type ii distribution\n", "\n", "\n", "\n", "benktander type ii distribution->weibull distribution\n", "\n", "\n", "\n", "\n", "\n", "behrens–fisher distribution\n", "\n", "behrens–fisher distribution\n", "\n", "\n", "\n", "behrens–fisher distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "gibbs distribution\n", "\n", "gibbs distribution\n", "\n", "\n", "\n", "gibbs distribution->maxwell–boltzmann distribution\n", "\n", "\n", "\n", "\n", "\n", "half-logistic distribution\n", "\n", "half-logistic distribution\n", "\n", "\n", "\n", "half-logistic distribution->logistic distribution\n", "\n", "\n", "\n", "\n", "\n", "logit-normal distribution\n", "\n", "logit-normal distribution\n", "\n", "\n", "\n", "logit-normal distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "maxwell's distribution\n", "\n", "maxwell's distribution\n", "\n", "\n", "\n", "maxwell–jüttner distribution\n", "\n", "maxwell–jüttner distribution\n", "\n", "\n", "\n", "maxwell–jüttner distribution->maxwell's distribution\n", "\n", "\n", "\n", "\n", "\n", "matrix-exponential distribution\n", "\n", "matrix-exponential distribution\n", "\n", "\n", "\n", "matrix-exponential distribution->phase-type distribution\n", "\n", "\n", "\n", "\n", "\n", "marshall–olkin exponential distribution\n", "\n", "marshall–olkin exponential distribution\n", "\n", "\n", "\n", "marshall–olkin exponential distribution->exponential distribution\n", "\n", "\n", "\n", "\n", "\n", "marchenko–pastur distribution\n", "\n", "marchenko–pastur distribution\n", "\n", "\n", "\n", "marchenko–pastur distribution->convergence in distribution\n", "\n", "\n", "\n", "\n", "\n", "hyper-erlang distribution\n", "\n", "hyper-erlang distribution\n", "\n", "\n", "\n", "hyper-erlang distribution->erlang distribution\n", "\n", "\n", "\n", "\n", "\n", "log-cauchy distribution\n", "\n", "log-cauchy distribution\n", "\n", "\n", "\n", "log-cauchy distribution->cauchy distribution\n", "\n", "\n", "\n", "\n", "\n", "landau distribution\n", "\n", "landau distribution\n", "\n", "\n", "\n", "landau distribution->stable distribution\n", "\n", "\n", "\n", "\n", "\n", "kumaraswamy distribution\n", "\n", "kumaraswamy distribution\n", "\n", "\n", "\n", "kumaraswamy distribution->beta distribution\n", "\n", "\n", "\n", "\n", "\n", "joint distribution\n", "\n", "joint distribution\n", "\n", "\n", "\n", "joint distribution->conditional probability distribution\n", "\n", "\n", "\n", "\n", "\n", "johnson su distribution\n", "\n", "johnson su distribution\n", "\n", "\n", "\n", "johnson su distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "johnson's su-distribution\n", "\n", "johnson's su-distribution\n", "\n", "\n", "\n", "johnson's su-distribution->normal distribution\n", "\n", "\n", "\n", "\n", "\n", "inverse-wishart distribution\n", "\n", "inverse-wishart distribution\n", "\n", "\n", "\n", "inverse-wishart distribution->wishart distribution\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "node_selection = df_degree['node'].tolist()\n", "\n", "graph = plot_network(node_selection, size='15')\n", "graph" ] }, { "cell_type": "code", "execution_count": 17, "id": "vertical-surgeon", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "'distribution_landscape.pdf'" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# save the whole network for posterity\n", "graph.render('distribution_landscape', view=False, cleanup=True)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.6" }, "toc-autonumbering": true }, "nbformat": 4, "nbformat_minor": 5 }