{"id":216,"date":"2023-08-04T02:39:23","date_gmt":"2023-08-04T02:39:23","guid":{"rendered":"https:\/\/statorials.org\/tr\/beta-dagilimi\/"},"modified":"2023-08-04T02:39:23","modified_gmt":"2023-08-04T02:39:23","slug":"beta-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/beta-dagilimi\/","title":{"rendered":"Beta da\u011f\u0131l\u0131m\u0131"},"content":{"rendered":"<p>Bu makalede beta da\u011f\u0131t\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayn\u0131 \u015fekilde beta da\u011f\u0131l\u0131m grafi\u011fini ve bu tip olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerini g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-beta\"><\/span> Beta da\u011f\u0131l\u0131m\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Beta da\u011f\u0131l\u0131m\u0131,<\/strong> (0,1) aral\u0131\u011f\u0131nda tan\u0131mlanan ve iki pozitif parametreyle parametrelendirilen bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r: \u03b1 ve \u03b2. Yani beta da\u011f\u0131l\u0131m\u0131n\u0131n de\u011ferleri \u03b1 ve \u03b2 parametrelerine ba\u011fl\u0131d\u0131r.<\/p>\n<p> Bu nedenle beta da\u011f\u0131l\u0131m\u0131n\u0131n temel \u00f6zelli\u011fi, \u015feklinin \u03b1 ve \u03b2 parametreleri taraf\u0131ndan kontrol edilebilmesidir. Ayr\u0131ca beta da\u011f\u0131l\u0131m\u0131, de\u011feri 0 ile 1 aras\u0131nda olan rastgele de\u011fi\u015fkenleri tan\u0131mlamak i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> S\u00fcrekli bir rastgele de\u011fi\u015fkenin beta da\u011f\u0131l\u0131m\u0131 taraf\u0131ndan y\u00f6netildi\u011fini g\u00f6steren \u00e7e\u015fitli g\u00f6sterimler vard\u0131r, en yayg\u0131n olanlar\u0131 \u015funlard\u0131r:<\/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> \u0130statistikte beta da\u011f\u0131l\u0131m\u0131n\u0131n \u00e7ok \u00e7e\u015fitli uygulamalar\u0131 vard\u0131r. \u00d6rne\u011fin beta da\u011f\u0131l\u0131m\u0131, farkl\u0131 \u00f6rneklerdeki y\u00fczdelerdeki de\u011fi\u015fiklikleri incelemek i\u00e7in kullan\u0131l\u0131r. Benzer \u015fekilde proje y\u00f6netiminde Pert analizini ger\u00e7ekle\u015ftirmek i\u00e7in beta da\u011f\u0131t\u0131m\u0131 kullan\u0131l\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-beta\"><\/span> Beta da\u011f\u0131t\u0131m grafi\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Beta da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131 dikkate al\u0131narak beta da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu ve olas\u0131l\u0131k da\u011f\u0131l\u0131m fonksiyonu a\u015fa\u011f\u0131da \u00e7izilmi\u015ftir.<\/p>\n<p> A\u015fa\u011f\u0131da beta da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu grafi\u011finin \u03b1 ve \u03b2 parametrelerine ba\u011fl\u0131 olarak nas\u0131l de\u011fi\u015fti\u011fini g\u00f6rebilirsiniz. <\/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=\"beta da\u011f\u0131t\u0131m tablosu\" class=\"wp-image-4315\" width=\"621\" height=\"372\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Benzer \u015fekilde, a\u015fa\u011f\u0131da \u03b1 ve \u03b2 parametrelerine dayal\u0131 olarak beta da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131n\u0131n grafiksel g\u00f6sterimini g\u00f6rebilirsiniz. <\/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=\"k\u00fcm\u00fclatif beta da\u011f\u0131l\u0131m tablosu\" class=\"wp-image-4316\" width=\"621\" height=\"373\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-beta\"><\/span> Beta da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu b\u00f6l\u00fcmde beta da\u011f\u0131l\u0131m\u0131n\u0131n en \u00f6nemli \u00f6zelliklerinin neler oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<ul>\n<li> Beta da\u011f\u0131l\u0131m\u0131n\u0131n \u03b1 ve \u03b2 parametreleri ger\u00e7ek ve pozitif say\u0131lard\u0131r.<\/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> Beta da\u011f\u0131l\u0131m\u0131n\u0131n alan\u0131 0 ile 1 aras\u0131nda de\u011fi\u015fir; iki u\u00e7 nokta dahil de\u011fildir.<\/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> Beta da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131, alfa b\u00f6l\u00fc alfa art\u0131 beta toplam\u0131na e\u015fittir.<\/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> Beta da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131 a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplanabilir:<\/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> Alfa ve betan\u0131n 1&#8217;den b\u00fcy\u00fck de\u011ferleri i\u00e7in beta da\u011f\u0131l\u0131m modu a\u015fa\u011f\u0131daki ifadeyle kolayl\u0131kla bulunabilir:<\/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> Beta da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu a\u015fa\u011f\u0131daki gibidir:<\/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> Burada B(\u03b1,\u03b2) beta fonksiyonudur ve \u015fu \u015fekilde tan\u0131mlan\u0131r:<\/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> Beta da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonu \u015f\u00f6yledir:<\/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> Burada B(x;\u03b1,\u03b2) tamamlanmam\u0131\u015f beta fonksiyonudur ve \u015fu \u015fekilde tan\u0131mlan\u0131r:<\/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> X, bir beta da\u011f\u0131l\u0131m\u0131 taraf\u0131ndan tan\u0131mlanan bir de\u011fi\u015fkense, 1-X, alfa ve beta parametreleri s\u0131ras\u0131yla orijinal beta da\u011f\u0131l\u0131m\u0131n\u0131n beta ve alfa parametreleri olan bir beta da\u011f\u0131l\u0131m\u0131 taraf\u0131ndan tan\u0131mlanan bir de\u011fi\u015fkendir.<\/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> Beta da\u011f\u0131l\u0131m\u0131n\u0131n alfa ve beta parametrelerinin her ikisi de 1&#8217;e e\u015fitse, bu durumda da\u011f\u0131l\u0131m, 0 ve 1 parametrelerinin d\u00fczg\u00fcn bir da\u011f\u0131l\u0131m\u0131na e\u015fde\u011ferdir.<\/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>Bu makalede beta da\u011f\u0131t\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayn\u0131 \u015fekilde beta da\u011f\u0131l\u0131m grafi\u011fini ve bu tip olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerini g\u00f6rebileceksiniz. Beta da\u011f\u0131l\u0131m\u0131 nedir? Beta da\u011f\u0131l\u0131m\u0131, (0,1) aral\u0131\u011f\u0131nda tan\u0131mlanan ve iki pozitif parametreyle parametrelendirilen bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r: \u03b1 ve \u03b2. Yani beta da\u011f\u0131l\u0131m\u0131n\u0131n de\u011ferleri \u03b1 ve \u03b2 parametrelerine ba\u011fl\u0131d\u0131r. Bu nedenle beta da\u011f\u0131l\u0131m\u0131n\u0131n [&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":[],"class_list":["post-216","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Beta Da\u011f\u0131l\u0131m\u0131 - Olas\u0131l\u0131klar ve \u0130statistikler<\/title>\n<meta name=\"description\" content=\"Bu makalede beta da\u011f\u0131t\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayn\u0131 \u015fekilde beta da\u011f\u0131l\u0131m grafi\u011fini ve \u00f6zelliklerini g\u00f6rebileceksiniz \u2705\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/beta-dagilimi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Beta Da\u011f\u0131l\u0131m\u0131 - Olas\u0131l\u0131klar ve \u0130statistikler\" \/>\n<meta property=\"og:description\" content=\"Bu makalede beta da\u011f\u0131t\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayn\u0131 \u015fekilde beta da\u011f\u0131l\u0131m grafi\u011fini ve \u00f6zelliklerini g\u00f6rebileceksiniz \u2705\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/beta-dagilimi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-04T02:39:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ee1d0d8a1624a017b8ef9ce8a67c694e_l3.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/beta-dagilimi\/\",\"url\":\"https:\/\/statorials.org\/tr\/beta-dagilimi\/\",\"name\":\"\u25b7 Beta Da\u011f\u0131l\u0131m\u0131 - Olas\u0131l\u0131klar ve \u0130statistikler\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-04T02:39:23+00:00\",\"dateModified\":\"2023-08-04T02:39:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu makalede beta da\u011f\u0131t\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. 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