{"id":4084,"date":"2026-10-15T07:39:02","date_gmt":"2026-10-15T06:39:02","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/istatistik\/beta-dagilimi-hesaplayicisi\/"},"modified":"2026-10-15T07:39:02","modified_gmt":"2026-10-15T06:39:02","slug":"beta-dagilimi-hesaplayicisi","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/beta-dagilimi-hesaplayicisi\/","title":{"rendered":"Beta da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Beta olas\u0131l\u0131klar\u0131n\u0131, yo\u011funlu\u011funu ve momentlerini hesaplay\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4084\" data-favorite-title=\"Beta da\u011f\u0131l\u0131m\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/beta-dagilimi-hesaplayicisi\/\" data-favorite-excerpt=\"0 ile 1 aras\u0131ndaki herhangi bir oran i\u00e7in beta da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funlu\u011funu, birikimli ve kuyruk olas\u0131l\u0131klar\u0131n\u0131, aral\u0131k olas\u0131l\u0131\u011f\u0131n\u0131, ortalamas\u0131n\u0131, varyans\u0131n\u0131 ve modunu hesaplamak \u00fczere \u03b1 ve \u03b2 \u015fekil parametrelerini girin.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-wpcalc-distribution-histogram\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/istatistik\/beta-dagilimi-hesaplayicisi\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4084\" data-post=\"4084\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Alfa \u015fekil parametresi<\/label><div class=\"term\">\u03b1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"alfa_ekil_parametresi\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 2\" min=\"0.01\" value=\"2\"\/><small id=\"calc-info-1\">\u015eekil parametresi \u03b1 &gt; 0: 1&#039;e yak\u0131n de\u011ferlerin a\u011f\u0131rl\u0131\u011f\u0131n\u0131 belirler. \u03b1 = \u03b2 = 1 oldu\u011funda [0, 1] aral\u0131\u011f\u0131nda d\u00fczg\u00fcn da\u011f\u0131l\u0131m elde edilir.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Beta \u015fekil parametresi<\/label><div class=\"term\">\u03b2<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"beta_ekil_parametresi\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0.01\" value=\"5\"\/><small id=\"calc-info-2\">\u015eekil parametresi \u03b2 &gt; 0: 0&#039;a yak\u0131n de\u011ferlerin a\u011f\u0131rl\u0131\u011f\u0131n\u0131 belirler.<\/small><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Hesaplanacak de\u011fer<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"hesaplanacak_deer\"><option value=\"point\" selected>Tek bir x oran\u0131nda<\/option><option value=\"interval\">[a, b] aral\u0131\u011f\u0131nda<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-4\">Oran<\/label><div class=\"term\">x<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"oran\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.3\" min=\"0\" max=\"1\" value=\"0.3\"\/><small id=\"calc-info-4\">Hesaplama yap\u0131lacak 0 ile 1 aras\u0131ndaki x de\u011feri; \u00f6rne\u011fin bir oran, pay veya olas\u0131l\u0131k.<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">Alt s\u0131n\u0131r<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"alt_snr\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.2\" min=\"0\" max=\"1\" value=\"0.2\"\/><small id=\"calc-info-5\">Aral\u0131\u011f\u0131n ba\u015flang\u0131c\u0131 (0 ile 1 aras\u0131nda).<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">\u00dcst s\u0131n\u0131r<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"st_snr\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.5\" min=\"0\" max=\"1\" value=\"0.5\"\/><small id=\"calc-info-6\">Aral\u0131\u011f\u0131n biti\u015fi; alt s\u0131n\u0131rdan b\u00fcy\u00fck olmal\u0131d\u0131r.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4084\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Beta da\u011f\u0131l\u0131m\u0131 sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Orandaki yo\u011funluk<\/span><span class=\"result-term\">f(x)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Birikimli olas\u0131l\u0131k P(X \u2264 x)<\/span><span class=\"result-term\">F(x)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>\u00dcst kuyruk olas\u0131l\u0131\u011f\u0131 P(X &gt; x)<\/span><span class=\"result-term\">S(x)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Aral\u0131k olas\u0131l\u0131\u011f\u0131 P(a \u2264 X \u2264 b)<\/span><span class=\"result-term\">P(a\u2264X\u2264b)<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Ortalama<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Varyans<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-7\"><span class=\"field-title\"><span>Mod (en olas\u0131 de\u011fer)<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-8\"><span class=\"field-title\"><span>Hesaplama y\u00f6ntemi ve sonu\u00e7lar\u0131n yorumu<\/span><\/span><span class=\"field-value\" id=\"result-8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4084\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Beta da\u011f\u0131l\u0131m\u0131 form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\\[ f(x) = \\frac{x^{\u03b1-1}(1-x)^{\u03b2-1}}{B(\u03b1, \u03b2)}, \\quad F(x) = I_x(\u03b1, \u03b2), \\quad \\text{Ortalama} = \\frac{\u03b1}{\u03b1+\u03b2}, \\quad \u03c3^2 = \\frac{\u03b1\u03b2}{(\u03b1+\u03b2)^2(\u03b1+\u03b2+1)}, \\quad \\text{Mod} = \\frac{\u03b1-1}{\u03b1+\u03b2-2} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\u03b1, \u03b2 \u2014 her ikisi de 0'dan b\u00fcy\u00fck olan \u015fekil parametreleri<\/li>\n<li>\u03b1, 1'e yak\u0131n de\u011ferlerin; \u03b2 ise 0'a yak\u0131n de\u011ferlerin a\u011f\u0131rl\u0131\u011f\u0131n\u0131 belirler<\/li>\n<li>\u03b1 = \u03b2 = 1 oldu\u011funda [0, 1] aral\u0131\u011f\u0131nda d\u00fczg\u00fcn da\u011f\u0131l\u0131m elde edilir<\/li>\n<li>\u03b1 = \u03b2 oldu\u011funda merkezi 0,5 olan simetrik, \u00e7an e\u011frisi bi\u00e7iminde bir da\u011f\u0131l\u0131m elde edilir<\/li>\n<li>\u03b1, \u03b2 &lt; 1 oldu\u011funda olas\u0131l\u0131\u011f\u0131n iki u\u00e7 noktaya yak\u0131n de\u011ferlerde topland\u0131\u011f\u0131 U bi\u00e7iminde bir da\u011f\u0131l\u0131m elde edilir<\/li>\n<li>Mod yaln\u0131zca \u03b1 &gt; 1 ve \u03b2 &gt; 1 oldu\u011funda vard\u0131r<\/li>\n<\/ul>\n<p>Yo\u011funluk, [0, 1] aral\u0131\u011f\u0131ndaki her x oran\u0131n\u0131n Beta(\u03b1, \u03b2) da\u011f\u0131l\u0131m\u0131na g\u00f6re ne kadar olas\u0131 oldu\u011funu g\u00f6sterir. Birikimli da\u011f\u0131l\u0131m fonksiyonu F(x), d\u00fczenlenmi\u015f tamamlanmam\u0131\u015f beta fonksiyonu \\(I_x(\u03b1, \u03b2)\\) ile ifade edilir. Aral\u0131k olas\u0131l\u0131klar\u0131 ise \\(P(a \\le X \\le b) = F(b) - F(a)\\) ba\u011f\u0131nt\u0131s\u0131yla hesaplan\u0131r.<\/p>\n<p>Beta da\u011f\u0131l\u0131m\u0131; oranlar, paylar ve olas\u0131l\u0131klar gibi [0, 1] aral\u0131\u011f\u0131nda de\u011fer alan nicelikleri modellemek i\u00e7in yayg\u0131n olarak kullan\u0131l\u0131r. Bayes analizinde binom da\u011f\u0131l\u0131m\u0131ndaki ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 i\u00e7in do\u011fal \u00f6nsel ve sonsal da\u011f\u0131l\u0131md\u0131r.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Beta da\u011f\u0131l\u0131m\u0131 \u2013 hesaplama \u00f6rne\u011fi<\/h2><\/div>\r\n\r\n<p>{wp_code}<\/p>\n<p><strong>\u00d6rnek:<\/strong> Bir d\u00f6n\u00fc\u015f\u00fcm oran\u0131n\u0131n sonsal da\u011f\u0131l\u0131m\u0131 Beta(2, 5) olsun. Da\u011f\u0131l\u0131m\u0131 x = 0,3 noktas\u0131nda de\u011ferlendirelim.<\/p>\n<p>\\[ B(2, 5) = \\frac{\u0393(2)\u0393(5)}{\u0393(7)} = \\frac{1 \\cdot 24}{720} = \\frac{1}{30} \\]<\/p>\n<p>\\[ f(0.3) = 30 \\cdot 0.3^1 \\cdot 0.7^4 = 30 \\cdot 0.3 \\cdot 0.2401 = 2.1609 \\]<\/p>\n<p>\\[ F(0.3) = 1 - (1-0.3)^5(1 + 5 \\cdot 0.3) = 1 - 0.16807 \\cdot 2.5 = 0.57983 \\]<\/p>\n<p>\\[ \\text{Ortalama} = \\frac{2}{7} = 0.28571, \\quad \u03c3^2 = \\frac{10}{392} = 0.02551, \\quad \\text{Mod} = \\frac{1}{5} = 0.2 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> f(0,3) \u2248 2,1609; P(X \u2264 0,3) \u2248 0,57983 (%57,98); P(X &gt; 0,3) \u2248 0,42018; ortalama 0,28571; varyans 0,02551; mod 0,2. Aral\u0131k moduna ge\u00e7ip a = 0,2 ve b = 0,5 girildi\u011finde P(0,2 \u2264 X \u2264 0,5) = F(0,5) \u2212 F(0,2) = 0,89063 \u2212 0,34464 = 0,54599, yani yakla\u015f\u0131k %54,6 elde edilir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Alfa \u015fekil parametresini<\/strong> (\u03b1) ve <strong>Beta \u015fekil parametresini<\/strong> (\u03b2) girin. Her ikisi de pozitif olmal\u0131d\u0131r.<\/li>\n<li>Ne hesaplayaca\u011f\u0131n\u0131z\u0131 se\u00e7in: Bir noktadaki yo\u011funluk ve kuyruk olas\u0131l\u0131klar\u0131 i\u00e7in <strong>Tek bir x oran\u0131nda<\/strong>, iki oran aras\u0131ndaki olas\u0131l\u0131k i\u00e7in <strong>[a, b] aral\u0131\u011f\u0131nda<\/strong> se\u00e7ene\u011fini kullan\u0131n.<\/li>\n<li><strong>Oran<\/strong> x de\u011ferini (0 ile 1 aras\u0131nda) veya aral\u0131\u011f\u0131n <strong>Alt s\u0131n\u0131r\u0131n\u0131<\/strong> ve <strong>\u00dcst s\u0131n\u0131r\u0131n\u0131<\/strong> girin.<\/li>\n<li>Yo\u011funluk, birikimli olas\u0131l\u0131k P(X \u2264 x), \u00fcst kuyruk olas\u0131l\u0131\u011f\u0131 P(X &gt; x), aral\u0131k olas\u0131l\u0131\u011f\u0131, ortalama, varyans ve mod sonu\u00e7lar\u0131n\u0131 k\u0131sa a\u00e7\u0131klamalar\u0131yla birlikte inceleyin.<\/li>\n<\/ol>\n<h2>Beta da\u011f\u0131l\u0131m\u0131 nedir?<\/h2>\n<p>Beta da\u011f\u0131l\u0131m\u0131, [0, 1] aral\u0131\u011f\u0131nda tan\u0131ml\u0131 bir s\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 ailesidir. Bu s\u0131n\u0131rl\u0131 de\u011fer aral\u0131\u011f\u0131 sayesinde d\u00f6n\u00fc\u015f\u00fcm oran\u0131, pazar pay\u0131, test do\u011frulu\u011fu, kusurlu \u00fcr\u00fcn oran\u0131 veya bilinmeyen bir olas\u0131l\u0131\u011f\u0131n kendisi gibi kesir ya da y\u00fczdeyle ifade edilen nicelikleri modellemek i\u00e7in s\u0131k\u00e7a kullan\u0131l\u0131r.<\/p>\n<p>\u0130ki \u015fekil parametresi, da\u011f\u0131l\u0131ma geni\u015f bir bi\u00e7im \u00e7e\u015fitlili\u011fi kazand\u0131r\u0131r. \u03b1 = \u03b2 = 1 oldu\u011funda sabit yo\u011funluklu d\u00fczg\u00fcn da\u011f\u0131l\u0131m elde edilir. \u03b1 = \u03b2 &gt; 1 oldu\u011funda da\u011f\u0131l\u0131m, merkezi 0,5 olan simetrik bir \u00e7an e\u011frisi bi\u00e7imini al\u0131r. Parametreler e\u015fit de\u011filse da\u011f\u0131l\u0131m 0'a veya 1'e do\u011fru \u00e7arp\u0131kla\u015f\u0131r; her iki parametre de 1'in alt\u0131ndaysa olas\u0131l\u0131\u011f\u0131n u\u00e7 noktalara yak\u0131n topland\u0131\u011f\u0131 bir U bi\u00e7imi ortaya \u00e7\u0131kar. Bu esneklik nedeniyle beta da\u011f\u0131l\u0131m\u0131, Bayes istatisti\u011finden proje y\u00f6netimine (PERT) ve Bayes\u00e7i A\/B testlerine kadar pek \u00e7ok alanda kullan\u0131l\u0131r.<\/p>\n<p>En \u00f6nemli kullan\u0131m alan\u0131 Bayes\u00e7i \u00e7\u0131kar\u0131md\u0131r. Beta da\u011f\u0131l\u0131m\u0131, binom da\u011f\u0131l\u0131m\u0131n\u0131n <em>e\u015flenik \u00f6nsel da\u011f\u0131l\u0131m\u0131d\u0131r<\/em>: Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 i\u00e7in Beta(\u03b1\u2080, \u03b2\u2080) \u00f6nsel da\u011f\u0131l\u0131m\u0131yla ba\u015flay\u0131p s ba\u015far\u0131 ve n \u2212 s ba\u015far\u0131s\u0131zl\u0131k g\u00f6zlemlerseniz sonsal da\u011f\u0131l\u0131m tam olarak Beta(\u03b1\u2080 + s, \u03b2\u2080 + n \u2212 s) olur. \u00d6rne\u011fin, d\u00fczg\u00fcn Beta(1, 1) \u00f6nsel da\u011f\u0131l\u0131m\u0131 ve 20 denemede 5 ba\u015far\u0131, Beta(6, 16) sonsal da\u011f\u0131l\u0131m\u0131n\u0131 verir. Bu da\u011f\u0131l\u0131m\u0131n kuyruk olas\u0131l\u0131klar\u0131n\u0131 do\u011frudan bu hesaplay\u0131c\u0131dan g\u00f6rebilirsiniz; %95'lik bir g\u00fcvenilirlik aral\u0131\u011f\u0131, olas\u0131l\u0131k k\u00fctlesinin ortadaki %95'ini kapsar. Bu g\u00fcncellemenin temelindeki mant\u0131k i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/bayes-teoremi-hesaplama\/\">Bayes teoremi hesaplay\u0131c\u0131s\u0131na<\/a> bak\u0131n.<\/p>\n<h2>Sonu\u00e7lar nas\u0131l yorumlan\u0131r?<\/h2>\n<p><strong>Yo\u011funluk<\/strong> f(x), e\u011frinin x noktas\u0131ndaki y\u00fcksekli\u011fidir; tek ba\u015f\u0131na bir olas\u0131l\u0131k de\u011fildir, ancak de\u011ferinin y\u00fcksek olmas\u0131 x'e yak\u0131n de\u011ferlerin daha olas\u0131 oldu\u011funu g\u00f6sterir. <strong>Birikimli olas\u0131l\u0131k<\/strong> F(x), niceli\u011fin en fazla x olma olas\u0131l\u0131\u011f\u0131d\u0131r. <strong>\u00dcst kuyruk olas\u0131l\u0131\u011f\u0131<\/strong> ise bunun t\u00fcmleyeni olan 1 \u2212 F(x)'tir. Bu de\u011ferlerle \u201cD\u00f6n\u00fc\u015f\u00fcm oran\u0131n\u0131n %20'nin alt\u0131nda olma olas\u0131l\u0131\u011f\u0131 nedir?\u201d veya \u201c%30'u a\u015fma olas\u0131l\u0131\u011f\u0131 nedir?\u201d gibi sorular\u0131 yan\u0131tlayabilirsiniz.<\/p>\n<p><strong>Ortalama<\/strong> \u03b1\/(\u03b1+\u03b2), da\u011f\u0131l\u0131m\u0131n denge noktas\u0131d\u0131r; Bayes\u00e7i analizde ise oran\u0131n sonsal tahminidir. \u03b1 + \u03b2 b\u00fcy\u00fcd\u00fck\u00e7e <strong>varyans<\/strong> azal\u0131r. Bu nedenle daha fazla veriyle birlikte b\u00fcy\u00fcyen sonsal parametreler, daha kesin \u00e7\u0131kar\u0131mlar sa\u011flar. <strong>Mod<\/strong>, en olas\u0131 tek de\u011ferdir ve yaln\u0131zca iki parametre de 1'den b\u00fcy\u00fck oldu\u011funda vard\u0131r. \u03b1 = \u03b2 = 1 \u00f6zel durumunu g\u00f6rmek i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/duzgun-dagilim-hesaplayici\/\">D\u00fczg\u00fcn da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131yla<\/a>, \u00fcst s\u0131n\u0131r\u0131 olmayan benzer bir da\u011f\u0131l\u0131m\u0131 incelemek i\u00e7in de <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/gama-dagilimi-hesaplayici\/\">Gama da\u011f\u0131l\u0131m\u0131 hesaplay\u0131c\u0131s\u0131yla<\/a> kar\u015f\u0131la\u015ft\u0131r\u0131n.<\/p>\n<h2>\u0130pu\u00e7lar\u0131, varsay\u0131mlar ve s\u0131n\u0131rlamalar<\/h2>\n<ul>\n<li>Da\u011f\u0131l\u0131m yaln\u0131zca [0, 1] aral\u0131\u011f\u0131nda tan\u0131ml\u0131d\u0131r. \u0130nceledi\u011finiz nicelik daha geni\u015f bir aral\u0131kta de\u011fer al\u0131yorsa \u00f6nce \u00f6l\u00e7e\u011fini bu aral\u0131\u011fa d\u00f6n\u00fc\u015ft\u00fcr\u00fcn veya ba\u015fka bir da\u011f\u0131l\u0131m ailesi kullan\u0131n.<\/li>\n<li>\u015eekil parametreleri kesinlikle pozitif olmal\u0131d\u0131r. Hesaplay\u0131c\u0131, Bayes\u00e7i \u00f6nsel da\u011f\u0131l\u0131mlarda yayg\u0131n olan kesirli de\u011ferler de d\u00e2hil olmak \u00fczere her pozitif de\u011feri kabul eder (\u00f6rne\u011fin, Jeffreys \u00f6nsel da\u011f\u0131l\u0131m\u0131 Beta(0,5; 0,5)).<\/li>\n<li>\u03b1 &lt; 1 veya \u03b2 &lt; 1 oldu\u011funda yo\u011funluk, ilgili u\u00e7 noktada s\u0131n\u0131rs\u0131zd\u0131r (sonsuza gider). Hesaplay\u0131c\u0131n\u0131n bunu g\u00f6stermesi matematiksel olarak normaldir.<\/li>\n<li>Aral\u0131k modunda \u00fcst s\u0131n\u0131r alt s\u0131n\u0131rdan b\u00fcy\u00fck olmal\u0131 ve her iki s\u0131n\u0131r da [0, 1] aral\u0131\u011f\u0131nda bulunmal\u0131d\u0131r.<\/li>\n<li>Bayes\u00e7i uygulamalarda veri az oldu\u011funda \u00f6nsel parametrelerin se\u00e7imi \u00f6nemlidir. D\u00fczg\u00fcn Beta(1, 1) \u00f6nsel da\u011f\u0131l\u0131m\u0131 ile Jeffreys Beta(0,5; 0,5) \u00f6nsel da\u011f\u0131l\u0131m\u0131, yaln\u0131zca birka\u00e7 g\u00f6zlemden sonra belirgin bi\u00e7imde farkl\u0131 sonu\u00e7lar verebilir.<\/li>\n<li>T\u00fcmleyen birikimli de\u011fer S(x) = P(X &gt; x), tek tarafl\u0131 sorularda i\u015fe yarar. \u0130ki tarafl\u0131 sorular i\u00e7in do\u011frudan aral\u0131k modunu kullanabilirsiniz.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>0 ile 1 aras\u0131ndaki herhangi bir oran i\u00e7in beta da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funlu\u011funu, birikimli ve kuyruk olas\u0131l\u0131klar\u0131n\u0131, aral\u0131k olas\u0131l\u0131\u011f\u0131n\u0131, ortalamas\u0131n\u0131, varyans\u0131n\u0131 ve modunu hesaplamak \u00fczere \u03b1 ve \u03b2 \u015fekil parametrelerini girin.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[12],"tags":[34],"class_list":["post-4084","post","type-post","status-publish","format-standard","hentry","category-istatistik","tag-dagilimlar"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4084"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4084\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}