{"id":216,"date":"2023-08-04T02:39:23","date_gmt":"2023-08-04T02:39:23","guid":{"rendered":"https:\/\/statorials.org\/id\/distribusi-beta\/"},"modified":"2023-08-04T02:39:23","modified_gmt":"2023-08-04T02:39:23","slug":"distribusi-beta","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/distribusi-beta\/","title":{"rendered":"Distribusi beta"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi beta dan kegunaannya. Demikian pula, Anda akan dapat melihat grafik distribusi beta dan properti dari jenis distribusi probabilitas ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-beta\"><\/span> Apa distribusi beta?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi beta<\/strong> adalah distribusi probabilitas yang ditentukan pada interval (0,1) dan diparameterisasi oleh dua parameter positif: \u03b1 dan \u03b2. Dengan kata lain, nilai distribusi beta bergantung pada parameter \u03b1 dan \u03b2.<\/p>\n<p> Oleh karena itu, ciri utama distribusi beta adalah bentuknya dapat dikontrol oleh parameter \u03b1 dan \u03b2. Selain itu, distribusi beta digunakan untuk mendefinisikan variabel acak yang nilainya antara 0 dan 1.<\/p>\n<p> Ada beberapa notasi untuk menunjukkan bahwa variabel acak kontinu diatur oleh distribusi beta, yang paling umum adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ee1d0d8a1624a017b8ef9ce8a67c694e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex]X\\sim Beta(\\alpha,\\beta)\\\\[2ex]X\\sim \\beta_{\\alpha,\\beta}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"121\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Secara statistik, distribusi beta memiliki penerapan yang sangat bervariasi. Misalnya, distribusi beta digunakan untuk mempelajari variasi persentase dalam sampel yang berbeda. Demikian pula dalam manajemen proyek, distribusi beta digunakan untuk melakukan analisis Pert. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-beta\"><\/span> Plot distribusi beta<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Mengingat definisi distribusi beta, fungsi kepadatan dan fungsi distribusi probabilitas dari distribusi beta diplot di bawah ini.<\/p>\n<p> Di bawah ini Anda dapat melihat bagaimana grafik fungsi kepadatan distribusi beta bervariasi tergantung pada parameter \u03b1 dan \u03b2. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-graphique-beta.png\" alt=\"grafik distribusi beta\" class=\"wp-image-4315\" width=\"621\" height=\"372\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Demikian pula, di bawah ini Anda dapat melihat representasi grafis dari probabilitas kumulatif distribusi beta berdasarkan parameter \u03b1 dan \u03b2. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-beta-cumulative.png\" alt=\"grafik distribusi beta kumulatif\" class=\"wp-image-4316\" width=\"621\" height=\"373\" srcset=\"\" sizes=\"\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-beta\"><\/span> Karakteristik distribusi beta<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Di bagian ini kita akan melihat karakteristik terpenting dari distribusi beta.<\/p>\n<ul>\n<li> Parameter \u03b1 dan \u03b2 dari distribusi beta adalah bilangan real dan positif.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-442bebaba847543d6db71cdf0127a4b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\alpha >0\\\\[2ex] \\beta >0\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;54&#8243; width=&#8221;44&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Domain distribusi beta berkisar dari 0 hingga 1, dua ekstrem tidak termasuk.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-60f8667881e2c5a08eae2db3c3e04708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Rata-rata distribusi beta sama dengan alpha dibagi dengan jumlah alpha ditambah beta.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4530a8b72211111e8bec79b6388e00a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] E[X]=\\cfrac{\\alpha}{\\alpha+\\beta}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"111\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Varians distribusi beta dapat dihitung dengan menggunakan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-71c6ef40db833722e63c56cd763d6601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] Var(X)=\\cfrac{\\alpha\\cdot \\beta}{(\\alpha+\\beta+1)\\cdot (\\alpha+\\beta)^2}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Untuk nilai alpha dan beta lebih besar dari 1, mode distribusi beta dapat dengan mudah ditemukan dengan ekspresi berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-472cafc0cf9d1cf782206ddc7c9475d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=\\cfrac{\\alpha-1}{\\alpha+\\beta-2}\\qquad \\alpha,\\beta>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;42&#8243; width=&#8221;225&#8243; style=&#8221;vertical-align: -16px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Fungsi kepadatan distribusi beta adalah sebagai berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-48f1f2a13df23d7c779bc37da4b49368_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{x^{\\alpha-1}(1-x)^{\\beta-1}}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"218\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Dimana B(\u03b1,\u03b2) adalah fungsi beta, yang didefinisikan sebagai:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4eb1d2659d9993f9d05a35cce63fc14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(\\alpha,\\beta)=\\int_0^1x^{\\alpha-1}(1-x)^{\\beta-1}dx\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"248\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> Fungsi probabilitas kumulatif dari distribusi beta adalah:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-031b21ea3e2964d3ac4e6f222356d55b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{B(x;\\alpha,\\beta)}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Dimana B(x;\u03b1,\u03b2) adalah fungsi beta tidak lengkap, didefinisikan sebagai:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6c64764f48f86e8f97df5ed1e8d7fbe6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(x;\\,a,b) = \\int_0^x t^{a-1}\\,(1-t)^{b-1}\\,dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"255\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> Jika X adalah variabel yang ditentukan oleh distribusi beta, maka 1-X adalah variabel yang ditentukan oleh distribusi beta yang parameter alfa dan beta masing-masing merupakan parameter beta dan alfa dari distribusi beta asli.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c65dd399bb92ffe982784a6c1b6e5b0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(\\alpha,\\beta) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ 1-X\\sim B(\\beta,\\alpha)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"361\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Jika parameter alfa dan beta pada distribusi beta sama-sama sama dengan 1, maka distribusi tersebut ekuivalen dengan distribusi seragam parameter 0 dan 1.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-10010ad6c6959b44a8ae0fe4361b4034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(1,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim U(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi beta dan kegunaannya. Demikian pula, Anda akan dapat melihat grafik distribusi beta dan properti dari jenis distribusi probabilitas ini. Apa distribusi beta? Distribusi beta adalah distribusi probabilitas yang ditentukan pada interval (0,1) dan diparameterisasi oleh dua parameter positif: \u03b1 dan \u03b2. Dengan kata lain, nilai distribusi beta bergantung pada [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribusi Beta - Probabilitas dan Statistik<\/title>\n<meta name=\"description\" content=\"Artikel ini menjelaskan apa itu distribusi beta dan kegunaannya. 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