{"id":218,"date":"2023-08-04T01:54:33","date_gmt":"2023-08-04T01:54:33","guid":{"rendered":"https:\/\/statorials.org\/tr\/ki-kare-dagilimi\/"},"modified":"2023-08-04T01:54:33","modified_gmt":"2023-08-04T01:54:33","slug":"ki-kare-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ki-kare-dagilimi\/","title":{"rendered":"Ki-kare da\u011f\u0131l\u0131m\u0131"},"content":{"rendered":"<p>Bu makalede ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca ki-kare da\u011f\u0131l\u0131m grafi\u011fini ve \u00f6zelliklerini bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-chi-cuadrado\"><\/span> Ki-kare da\u011f\u0131l\u0131m\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ki-kare da\u011f\u0131l\u0131m\u0131<\/strong> sembol\u00fc \u03c7\u00b2 olan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Daha kesin olarak Ki-kare da\u011f\u0131l\u0131m\u0131, normal da\u011f\u0131l\u0131ma sahip <em>k<\/em> ba\u011f\u0131ms\u0131z rastgele de\u011fi\u015fkenin karelerinin toplam\u0131d\u0131r.<\/p>\n<p> Dolay\u0131s\u0131yla Ki-kare da\u011f\u0131l\u0131m\u0131 <em>k<\/em> serbestlik derecesine sahiptir. Bu nedenle, bir Ki-kare da\u011f\u0131l\u0131m\u0131, temsil etti\u011fi normal da\u011f\u0131l\u0131ml\u0131 de\u011fi\u015fkenlerin karelerinin toplam\u0131 kadar serbestlik derecesine sahiptir.<\/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-9ea0bf7a87071883ceae5e419bae9e71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X\\sim\\chi^2_k \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\begin{array}{l}\\text{Distribuci\\'on chi-cuadrado}\\\\[2ex]\\text{con k grados de libertad}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"404\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ki-kare da\u011f\u0131l\u0131m\u0131 <strong>Pearson da\u011f\u0131l\u0131m\u0131<\/strong> olarak da bilinir.<\/p>\n<p> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n gama da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zel bir durumu oldu\u011fu unutulmamal\u0131d\u0131r.<\/p>\n<p> Ki-kare da\u011f\u0131l\u0131m\u0131 istatistiksel \u00e7\u0131kar\u0131mlarda, \u00f6rne\u011fin hipotez testlerinde ve g\u00fcven aral\u0131klar\u0131nda yayg\u0131n olarak kullan\u0131l\u0131r. A\u015fa\u011f\u0131da bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n uygulamalar\u0131n\u0131n neler oldu\u011funu g\u00f6rece\u011fiz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-chi-cuadrado\"><\/span> Ki-kare da\u011f\u0131l\u0131m grafi\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra, bu t\u00fcr da\u011f\u0131l\u0131m\u0131n grafiksel olarak temsil edilen birka\u00e7 \u00f6rne\u011fini g\u00f6rece\u011fiz. A\u015fa\u011f\u0131da ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n olas\u0131l\u0131k grafi\u011finin serbestlik derecesine 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\/diagramme-de-distribution-du-chi-carre.png\" alt=\"ki-kare da\u011f\u0131l\u0131m grafi\u011fi\" class=\"wp-image-4212\" width=\"670\" height=\"405\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu yukar\u0131daki grafikte g\u00f6sterilmi\u015ftir. \u00d6te yandan ki-kare k\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m fonksiyonunun grafi\u011fi \u015fu \u015fekildedir: <\/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-du-chi-carre-cumulatif.png\" alt=\"ki-kare k\u00fcm\u00fclatif da\u011f\u0131l\u0131m grafi\u011fi\" class=\"wp-image-4215\" width=\"670\" height=\"405\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> Ki-kare da\u011f\u0131l\u0131m tablosu <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-chi-cuadrado\"><\/span> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu b\u00f6l\u00fcmde Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n olas\u0131l\u0131k teorisi ve istatisti\u011fe ili\u015fkin en \u00f6nemli \u00f6zelliklerini g\u00f6rece\u011fiz.<\/p>\n<ul>\n<li> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 serbestlik derecesine 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-8a7926aa60ec788064c47a5a34e641ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\chi^2_k\\\\[2ex] E[X]=k\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"73\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131, da\u011f\u0131l\u0131m\u0131n serbestlik derecesinin iki kat\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-cffd659f19d8ed8260fcaf53dc6dd83f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\chi^2_k\\\\[2ex] Var(X)=2\\cdot k\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Da\u011f\u0131t\u0131m birden fazla serbestlik derecesine sahip oldu\u011fu s\u00fcrece, ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n modu, serbestlik derecesinden iki birim daha azd\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-3c10387635aba8249e98afe0ca6f3ea9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=k-2 \\qquad \\text{si } k\\geq 2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"186\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> X=0 ise Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu s\u0131f\u0131rd\u0131r. Bununla birlikte, x&#8217;in 0&#8217;dan b\u00fcy\u00fck de\u011ferleri i\u00e7in Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu a\u015fa\u011f\u0131daki form\u00fclle tan\u0131mlan\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-f239003e822b2c8ba44146e94a94ad89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]= \\frac{(1\/2)^{k\/2}}{\\Gamma(k\/2)} x^{k\/2 - 1} e^{-x\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"254\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu a\u015fa\u011f\u0131daki form\u00fcle g\u00f6re y\u00f6netilir:<\/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-9d39bc2eb949e628c1109501656da4b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{\\gamma(k\/2,x\/2)}{\\Gamma(k\/2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"187\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n \u00e7arp\u0131kl\u0131k katsay\u0131s\u0131, sekiz b\u00f6l\u00fcm\u00fcn\u00fcn karek\u00f6k\u00fcn\u00fcn da\u011f\u0131l\u0131m\u0131n serbestlik derecesi say\u0131s\u0131na b\u00f6l\u00fcnmesiyle elde edilir.<\/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-c0113d9ec77836abace7fe06e18d90c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\sqrt{\\frac{8}{k}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"69\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<ul>\n<li> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n bas\u0131kl\u0131\u011f\u0131 a\u015fa\u011f\u0131daki ifade kullan\u0131larak hesaplan\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-a2c6ae2842ea42a7ff31babce8eb778a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C=3+\\cfrac{12}{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"88\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Merkezi limit teoremine ba\u011fl\u0131 olarak, e\u011fer <em>k<\/em> yeterince b\u00fcy\u00fckse, ki-kare da\u011f\u0131l\u0131m\u0131na normal bir da\u011f\u0131l\u0131mla yakla\u015f\u0131labilir. <\/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-b2c7e4c59f39b5f1910f7a7806c08819_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{k \\to \\infty} \\frac{\\chi^2_k (x)}{ k } = N_{\\left(1,\\sqrt{2\/k}\\right)} (x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"210\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-chi-cuadrado\"><\/span> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n uygulamalar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n istatistikte bir\u00e7ok farkl\u0131 uygulamas\u0131 vard\u0131r. Asl\u0131nda de\u011fi\u015fkenler aras\u0131ndaki ba\u011f\u0131ms\u0131zl\u0131\u011f\u0131 ve teorik da\u011f\u0131l\u0131ma uyumun iyili\u011fini kontrol etmek i\u00e7in kullan\u0131lan ki-kare testi bile vard\u0131r. \u00d6rne\u011fin, bir numunenin verilerinin Poisson da\u011f\u0131l\u0131m\u0131na uygun olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Ki-kare testi kullan\u0131labilir.<\/p>\n<p> Do\u011frusal regresyon analizinde ki-kare da\u011f\u0131l\u0131m\u0131, normal da\u011f\u0131l\u0131m g\u00f6steren bir pop\u00fclasyonun ortalamas\u0131n\u0131 tahmin etmek ve do\u011frusal regresyon \u00e7al\u0131\u015fma \u00e7izgisinin e\u011fimini tahmin etmek i\u00e7in de kullan\u0131l\u0131r.<\/p>\n<p> Son olarak Ki kare da\u011f\u0131l\u0131m\u0131, Snedecor F da\u011f\u0131l\u0131m\u0131 ile olan ili\u015fkisi nedeniyle varyans analizine de kat\u0131lmaktad\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca ki-kare da\u011f\u0131l\u0131m grafi\u011fini ve \u00f6zelliklerini bulacaks\u0131n\u0131z. Ki-kare da\u011f\u0131l\u0131m\u0131 nedir? Ki-kare da\u011f\u0131l\u0131m\u0131 sembol\u00fc \u03c7\u00b2 olan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Daha kesin olarak Ki-kare da\u011f\u0131l\u0131m\u0131, normal da\u011f\u0131l\u0131ma sahip k ba\u011f\u0131ms\u0131z rastgele de\u011fi\u015fkenin karelerinin toplam\u0131d\u0131r. Dolay\u0131s\u0131yla Ki-kare da\u011f\u0131l\u0131m\u0131 k serbestlik derecesine sahiptir. Bu nedenle, bir Ki-kare da\u011f\u0131l\u0131m\u0131, [&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-218","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 Ki kare da\u011f\u0131l\u0131m\u0131 (\u03c7\u00b2)<\/title>\n<meta name=\"description\" content=\"Burada Ki kare da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011funu, ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131, grafi\u011fini ve Ki kare da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerini bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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