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June 8, 2020 13:12
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| { | |
| "cells": [ | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "using Pkg\nPkg.add(\"Plots\")", | |
| "execution_count": 1, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": "\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m registry at `D:\\Users\\momma\\.julia\\registries\\General`\n" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "\u001b[?25l" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": "\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m git-repo `https://github.com/JuliaRegistries/General.git`\n" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "\u001b[2K\u001b[?25h" | |
| }, | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m FreeType2_jll ────── v2.10.1+2\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Reexport ─────────── v0.2.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Missings ─────────── v0.4.3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m FFMPEG_jll ───────── v4.1.0+3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m FixedPointNumbers ── v0.8.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m FFMPEG ───────────── v0.3.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m PlotUtils ────────── v1.0.4\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Plots ────────────── v1.3.7\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m NaNMath ──────────── v0.3.3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m libfdk_aac_jll ───── v0.1.6+2\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m LibVPX_jll ───────── v1.8.1+1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m OrderedCollections ─ v1.2.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m PlotThemes ───────── v2.0.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m StatsBase ────────── v0.33.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Contour ──────────── v0.5.3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m StaticArrays ─────── v0.12.3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Measures ─────────── v0.3.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m x265_jll ─────────── v3.0.0+1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m LAME_jll ─────────── v3.100.0+1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Showoff ──────────── v0.3.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m FriBidi_jll ──────── v1.0.5+3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Colors ───────────── v0.12.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m HTTP ─────────────── v0.8.15\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m GeometryTypes ────── v0.8.3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m IniFile ──────────── v0.5.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m SortingAlgorithms ── v0.3.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m RecipesBase ──────── v1.0.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m libass_jll ───────── v0.14.0+2\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Requires ─────────── v1.0.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m RecipesPipeline ──── v0.1.10\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m OpenSSL_jll ──────── v1.1.1+2\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m GR ───────────────── v0.50.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m x264_jll ─────────── v2019.5.25+2\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Opus_jll ─────────── v1.3.1+1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Bzip2_jll ────────── v1.0.6+2\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Ogg_jll ──────────── v1.3.4+0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m ColorTypes ───────── v0.10.3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m DataAPI ──────────── v1.3.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Zlib_jll ─────────── v1.2.11+10\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m DataStructures ───── v0.17.17\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m libvorbis_jll ────── v1.3.6+4\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m ColorSchemes ─────── v3.9.0\n\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `D:\\Users\\momma\\.julia\\environments\\v1.4\\Project.toml`\n \u001b[90m [91a5bcdd]\u001b[39m\u001b[92m + Plots v1.3.7\u001b[39m\n\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `D:\\Users\\momma\\.julia\\environments\\v1.4\\Manifest.toml`\n \u001b[90m [6e34b625]\u001b[39m\u001b[92m + Bzip2_jll v1.0.6+2\u001b[39m\n \u001b[90m [35d6a980]\u001b[39m\u001b[92m + ColorSchemes v3.9.0\u001b[39m\n \u001b[90m [3da002f7]\u001b[39m\u001b[92m + ColorTypes 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[c1c5ebd0]\u001b[39m\u001b[92m + LAME_jll v3.100.0+1\u001b[39m\n \u001b[90m [dd192d2f]\u001b[39m\u001b[92m + LibVPX_jll v1.8.1+1\u001b[39m\n \u001b[90m [442fdcdd]\u001b[39m\u001b[92m + Measures v0.3.1\u001b[39m\n \u001b[90m [e1d29d7a]\u001b[39m\u001b[92m + Missings v0.4.3\u001b[39m\n \u001b[90m [77ba4419]\u001b[39m\u001b[92m + NaNMath v0.3.3\u001b[39m\n \u001b[90m [e7412a2a]\u001b[39m\u001b[92m + Ogg_jll v1.3.4+0\u001b[39m\n \u001b[90m [458c3c95]\u001b[39m\u001b[92m + OpenSSL_jll v1.1.1+2\u001b[39m\n \u001b[90m [91d4177d]\u001b[39m\u001b[92m + Opus_jll v1.3.1+1\u001b[39m\n \u001b[90m [bac558e1]\u001b[39m\u001b[92m + OrderedCollections v1.2.0\u001b[39m\n \u001b[90m [ccf2f8ad]\u001b[39m\u001b[92m + PlotThemes v2.0.0\u001b[39m\n \u001b[90m [995b91a9]\u001b[39m\u001b[92m + PlotUtils v1.0.4\u001b[39m\n \u001b[90m [91a5bcdd]\u001b[39m\u001b[92m + Plots v1.3.7\u001b[39m\n \u001b[90m [3cdcf5f2]\u001b[39m\u001b[92m + RecipesBase v1.0.1\u001b[39m\n \u001b[90m [01d81517]\u001b[39m\u001b[92m + RecipesPipeline v0.1.10\u001b[39m\n \u001b[90m [189a3867]\u001b[39m\u001b[92m + Reexport v0.2.0\u001b[39m\n \u001b[90m [ae029012]\u001b[39m\u001b[92m + Requires v1.0.1\u001b[39m\n \u001b[90m [992d4aef]\u001b[39m\u001b[92m + Showoff v0.3.1\u001b[39m\n \u001b[90m [a2af1166]\u001b[39m\u001b[92m + SortingAlgorithms v0.3.1\u001b[39m\n \u001b[90m [90137ffa]\u001b[39m\u001b[92m + StaticArrays v0.12.3\u001b[39m\n \u001b[90m [2913bbd2]\u001b[39m\u001b[92m + StatsBase v0.33.0\u001b[39m\n \u001b[90m [83775a58]\u001b[39m\u001b[92m + Zlib_jll v1.2.11+10\u001b[39m\n \u001b[90m [0ac62f75]\u001b[39m\u001b[92m + libass_jll v0.14.0+2\u001b[39m\n \u001b[90m [f638f0a6]\u001b[39m\u001b[92m + libfdk_aac_jll v0.1.6+2\u001b[39m\n \u001b[90m [f27f6e37]\u001b[39m\u001b[92m + libvorbis_jll v1.3.6+4\u001b[39m\n \u001b[90m [1270edf5]\u001b[39m\u001b[92m + x264_jll v2019.5.25+2\u001b[39m\n \u001b[90m [dfaa095f]\u001b[39m\u001b[92m + x265_jll v3.0.0+1\u001b[39m\n \u001b[90m [8bb1440f]\u001b[39m\u001b[92m + DelimitedFiles \u001b[39m\n \u001b[90m [37e2e46d]\u001b[39m\u001b[92m + LinearAlgebra \u001b[39m\n \u001b[90m [2f01184e]\u001b[39m\u001b[92m + SparseArrays \u001b[39m\n \u001b[90m [10745b16]\u001b[39m\u001b[92m + Statistics \u001b[39m\n\u001b[32m\u001b[1m Building\u001b[22m\u001b[39m GR ───→ `D:\\Users\\momma\\.julia\\packages\\GR\\Atztx\\deps\\build.log`\n\u001b[32m\u001b[1m Building\u001b[22m\u001b[39m Plots → `D:\\Users\\momma\\.julia\\packages\\Plots\\Xnzc7\\deps\\build.log`\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "using Plots; gr()", | |
| "execution_count": 2, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": "┌ Info: Precompiling Plots [91a5bcdd-55d7-5caf-9e0b-520d859cae80]\n└ @ Base loading.jl:1260\n" | |
| }, | |
| { | |
| "data": { | |
| "text/plain": "Plots.GRBackend()" | |
| }, | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "Pkg.add(\"SpecialFunctions\")", | |
| "execution_count": 3, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m CompilerSupportLibraries_jll ─ v0.3.3+0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m OpenSpecFun_jll ────────────── v0.5.3+3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m SpecialFunctions ───────────── v0.10.3\n\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `D:\\Users\\momma\\.julia\\environments\\v1.4\\Project.toml`\n \u001b[90m [276daf66]\u001b[39m\u001b[92m + SpecialFunctions v0.10.3\u001b[39m\n\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `D:\\Users\\momma\\.julia\\environments\\v1.4\\Manifest.toml`\n \u001b[90m [e66e0078]\u001b[39m\u001b[92m + CompilerSupportLibraries_jll v0.3.3+0\u001b[39m\n \u001b[90m [efe28fd5]\u001b[39m\u001b[92m + OpenSpecFun_jll v0.5.3+3\u001b[39m\n \u001b[90m [276daf66]\u001b[39m\u001b[92m + SpecialFunctions v0.10.3\u001b[39m\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "using SpecialFunctions", | |
| "execution_count": 4, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": "┌ Info: Precompiling SpecialFunctions [276daf66-3868-5448-9aa4-cd146d93841b]\n└ @ Base loading.jl:1260\n" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "?Beta", | |
| "execution_count": 5, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "search: \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m_inc \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m_inc_inv l\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m nc\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m log\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m loga\u001b[0m\u001b[1mb\u001b[22msb\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m issu\u001b[0m\u001b[1mb\u001b[22ms\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\n\nCouldn't find \u001b[36mBeta\u001b[39m\nPerhaps you meant beta, eta, zeta, Meta, lbeta, Set, get, get!, let or ncbeta\n" | |
| }, | |
| { | |
| "data": { | |
| "text/latex": "No documentation found.\n\nBinding \\texttt{Beta} does not exist.\n\n", | |
| "text/markdown": "No documentation found.\n\nBinding `Beta` does not exist.\n", | |
| "text/plain": " No documentation found.\n\n Binding \u001b[36mBeta\u001b[39m does not exist." | |
| }, | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ] | |
| }, | |
| { | |
| "metadata": { | |
| "trusted": true | |
| }, | |
| "cell_type": "code", | |
| "source": "?beta", | |
| "execution_count": 6, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": "search: \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m_inc \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m_inc_inv l\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m nc\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m log\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m loga\u001b[0m\u001b[1mb\u001b[22msb\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m issu\u001b[0m\u001b[1mb\u001b[22ms\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\n\n" | |
| }, | |
| { | |
| "data": { | |
| "text/latex": "\\begin{verbatim}\nbeta(x, y)\n\\end{verbatim}\nEuler integral of the first kind $\\operatorname{B}(x,y) = \\Gamma(x)\\Gamma(y)/\\Gamma(x+y)$.\n\n", | |
| "text/markdown": "```\nbeta(x, y)\n```\n\nEuler integral of the first kind $\\operatorname{B}(x,y) = \\Gamma(x)\\Gamma(y)/\\Gamma(x+y)$.\n", | |
| "text/plain": "\u001b[36m beta(x, y)\u001b[39m\n\n Euler integral of the first kind \u001b[35m\\operatorname{B}(x,y) =\n \\Gamma(x)\\Gamma(y)/\\Gamma(x+y)\u001b[39m." | |
| }, | |
| "execution_count": 6, | |
| "metadata": {}, | |
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| "source": "Pkg.add(\"Distributions\")", | |
| "execution_count": 7, | |
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| "output_type": "stream", | |
| "text": "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Rmath ───────── v0.6.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m QuadGK ──────── v2.3.1\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m FillArrays ──── v0.8.10\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Rmath_jll ───── v0.2.2+0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Arpack ──────── v0.4.0\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Arpack_jll ──── v3.5.0+3\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m StatsFuns ───── v0.9.5\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Distributions ─ v0.23.4\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m PDMats ──────── v0.9.12\n\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m OpenBLAS_jll ── v0.3.9+4\n\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `D:\\Users\\momma\\.julia\\environments\\v1.4\\Project.toml`\n \u001b[90m [31c24e10]\u001b[39m\u001b[92m + Distributions v0.23.4\u001b[39m\n\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `D:\\Users\\momma\\.julia\\environments\\v1.4\\Manifest.toml`\n \u001b[90m [7d9fca2a]\u001b[39m\u001b[92m + Arpack v0.4.0\u001b[39m\n \u001b[90m [68821587]\u001b[39m\u001b[92m + Arpack_jll v3.5.0+3\u001b[39m\n \u001b[90m [31c24e10]\u001b[39m\u001b[92m + Distributions v0.23.4\u001b[39m\n \u001b[90m [1a297f60]\u001b[39m\u001b[92m + FillArrays v0.8.10\u001b[39m\n \u001b[90m [4536629a]\u001b[39m\u001b[92m + OpenBLAS_jll v0.3.9+4\u001b[39m\n \u001b[90m [90014a1f]\u001b[39m\u001b[92m + PDMats v0.9.12\u001b[39m\n \u001b[90m [1fd47b50]\u001b[39m\u001b[92m + QuadGK v2.3.1\u001b[39m\n \u001b[90m [79098fc4]\u001b[39m\u001b[92m + Rmath v0.6.1\u001b[39m\n \u001b[90m [f50d1b31]\u001b[39m\u001b[92m + Rmath_jll v0.2.2+0\u001b[39m\n \u001b[90m [4c63d2b9]\u001b[39m\u001b[92m + StatsFuns v0.9.5\u001b[39m\n \u001b[90m [4607b0f0]\u001b[39m\u001b[92m + SuiteSparse \u001b[39m\n" | |
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| "text": "┌ Info: Precompiling Distributions [31c24e10-a181-5473-b8eb-7969acd0382f]\n└ @ Base loading.jl:1260\n" | |
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| "source": "?Beta", | |
| "execution_count": 9, | |
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| "text": "search: \u001b[0m\u001b[1mB\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m_inc \u001b[0m\u001b[1mB\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22mPrime \u001b[0m\u001b[1mB\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22mBinomial \u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m_inc_inv l\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m nc\u001b[0m\u001b[1mb\u001b[22m\u001b[0m\u001b[1me\u001b[22m\u001b[0m\u001b[1mt\u001b[22m\u001b[0m\u001b[1ma\u001b[22m\n\n" | |
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| "text/latex": "\\begin{verbatim}\nBeta(α,β)\n\\end{verbatim}\nThe \\emph{Beta distribution} has probability density function\n\n$$f(x; \\alpha, \\beta) = \\frac{1}{B(\\alpha, \\beta)}\n x^{\\alpha - 1} (1 - x)^{\\beta - 1}, \\quad x \\in [0, 1]$$\nThe Beta distribution is related to the \\href{@ref}{\\texttt{Gamma}} distribution via the property that if $X \\sim \\operatorname{Gamma}(\\alpha)$ and $Y \\sim \\operatorname{Gamma}(\\beta)$ independently, then $X / (X + Y) \\sim Beta(\\alpha, \\beta)$.\n\n\\begin{verbatim}\nBeta() # equivalent to Beta(1, 1)\nBeta(a) # equivalent to Beta(a, a)\nBeta(a, b) # Beta distribution with shape parameters a and b\n\nparams(d) # Get the parameters, i.e. (a, b)\n\\end{verbatim}\nExternal links\n\n\\begin{itemize}\n\\item \\href{http://en.wikipedia.org/wiki/Beta_distribution}{Beta distribution on Wikipedia}\n\n\\end{itemize}\n", | |
| "text/markdown": "```\nBeta(α,β)\n```\n\nThe *Beta distribution* has probability density function\n\n$$\nf(x; \\alpha, \\beta) = \\frac{1}{B(\\alpha, \\beta)}\n x^{\\alpha - 1} (1 - x)^{\\beta - 1}, \\quad x \\in [0, 1]\n$$\n\nThe Beta distribution is related to the [`Gamma`](@ref) distribution via the property that if $X \\sim \\operatorname{Gamma}(\\alpha)$ and $Y \\sim \\operatorname{Gamma}(\\beta)$ independently, then $X / (X + Y) \\sim Beta(\\alpha, \\beta)$.\n\n```julia\nBeta() # equivalent to Beta(1, 1)\nBeta(a) # equivalent to Beta(a, a)\nBeta(a, b) # Beta distribution with shape parameters a and b\n\nparams(d) # Get the parameters, i.e. (a, b)\n```\n\nExternal links\n\n * [Beta distribution on Wikipedia](http://en.wikipedia.org/wiki/Beta_distribution)\n", | |
| "text/plain": "\u001b[36m Beta(α,β)\u001b[39m\n\n The \u001b[4mBeta distribution\u001b[24m has probability density function\n\n\u001b[35mf(x; \\alpha, \\beta) = \\frac{1}{B(\\alpha, \\beta)}\u001b[39m\n\u001b[35m x^{\\alpha - 1} (1 - x)^{\\beta - 1}, \\quad x \\in [0, 1]\u001b[39m\n\n The Beta distribution is related to the \u001b[36mGamma\u001b[39m distribution via the property\n that if \u001b[35mX \\sim \\operatorname{Gamma}(\\alpha)\u001b[39m and \u001b[35mY \\sim\n \\operatorname{Gamma}(\\beta)\u001b[39m independently, then \u001b[35mX / (X + Y) \\sim\n Beta(\\alpha, \\beta)\u001b[39m.\n\n\u001b[36m Beta() # equivalent to Beta(1, 1)\u001b[39m\n\u001b[36m Beta(a) # equivalent to Beta(a, a)\u001b[39m\n\u001b[36m Beta(a, b) # Beta distribution with shape parameters a and b\u001b[39m\n\u001b[36m \u001b[39m\n\u001b[36m params(d) # Get the parameters, i.e. (a, b)\u001b[39m\n\n External links\n\n • Beta distribution on Wikipedia\n (http://en.wikipedia.org/wiki/Beta_distribution)" | |
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| "execution_count": 9, | |
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| "cell_type": "code", | |
| "source": "X = 0.0:0.01:1.0", | |
| "execution_count": 13, | |
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| "data": { | |
| "text/plain": "0.0:0.01:1.0" | |
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| "cell_type": "code", | |
| "source": "c = 0.1\nf(c, x) = pdf(Beta(c, c), x)\nY = [f.(c, X) for c in 1.0:-0.1:0.1]", | |
| "execution_count": 16, | |
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| "data": { | |
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| "execution_count": 20, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
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| "Stacktrace:", | |
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