{"id":225,"date":"2023-08-03T23:58:33","date_gmt":"2023-08-03T23:58:33","guid":{"rendered":"https:\/\/statorials.org\/tr\/gama-dagilimi\/"},"modified":"2023-08-03T23:58:33","modified_gmt":"2023-08-03T23:58:33","slug":"gama-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/gama-dagilimi\/","title":{"rendered":"Gama da\u011f\u0131l\u0131m\u0131"},"content":{"rendered":"<p>Bu makalede gama da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece gama da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131, \u00f6zelliklerini ve grafik g\u00f6steriminin nas\u0131l g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-gamma\"><\/span> Gama da\u011f\u0131l\u0131m\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Gama da\u011f\u0131l\u0131m\u0131,<\/strong> iki karakteristik parametre olan \u03b1 ve \u03bb ile tan\u0131mlanan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Ba\u015fka bir deyi\u015fle, gama da\u011f\u0131l\u0131m\u0131 iki parametresinin de\u011ferine ba\u011fl\u0131d\u0131r: \u03b1 \u015fekil parametresidir ve \u03bb \u00f6l\u00e7ek parametresidir.<\/p>\n<p> Gama da\u011f\u0131l\u0131m\u0131n\u0131n sembol\u00fc b\u00fcy\u00fck Yunan harfi \u0393&#8217;dir. Yani bir rastgele de\u011fi\u015fken gama da\u011f\u0131l\u0131m\u0131n\u0131 takip ediyorsa \u015fu \u015fekilde yaz\u0131l\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-1b0ab2e724ffd74455d0907b39f4a598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(\\alpha,\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Gama da\u011f\u0131l\u0131m\u0131 ayr\u0131ca \u015fekil parametresi k = \u03b1 ve ters \u00f6l\u00e7ek parametresi \u03b8 = 1\/\u03bb kullan\u0131larak parametrelendirilebilir. Her durumda gama da\u011f\u0131l\u0131m\u0131n\u0131 tan\u0131mlayan iki parametre pozitif ger\u00e7ek say\u0131lard\u0131r.<\/p>\n<p> Tipik olarak gama da\u011f\u0131l\u0131m\u0131 sa\u011fa \u00e7arp\u0131k veri k\u00fcmelerini modellemek i\u00e7in kullan\u0131l\u0131r, b\u00f6ylece grafi\u011fin sol taraf\u0131nda daha fazla veri konsantrasyonu olur. \u00d6rne\u011fin, gama da\u011f\u0131l\u0131m\u0131 elektrikli bile\u015fenlerin g\u00fcvenilirli\u011fini modellemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-gamma\"><\/span> Gama da\u011f\u0131l\u0131m diyagram\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Gama da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011fi, karakteristik parametrelerinin de\u011ferlerine ba\u011fl\u0131d\u0131r. A\u015fa\u011f\u0131da gama da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonunun \u015fekil parametresine ve \u00f6l\u00e7ek parametresine 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\/trace-de-distribution-gamma.png\" alt=\"gama da\u011f\u0131l\u0131m tablosu\" class=\"wp-image-4536\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6te yandan gama da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonunun grafi\u011fini a\u015fa\u011f\u0131da 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-gamma-probabilite-cumulative.png\" alt=\"Gamm da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonunun grafi\u011fi\" class=\"wp-image-4537\" width=\"648\" height=\"388\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-gamma\"><\/span> Gama da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Daha sonra gama da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerinin neler oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<ul>\n<li> Gama da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011fi tamamen iki karakteristik parametresi ile tan\u0131mlan\u0131r: \u03b1 \u015fekil parametresidir ve \u03bb \u00f6l\u00e7ek parametresidir.<\/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-9640d41832cbcef7d0a7791c55ace57e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha , \\lambda >0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;62&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Gama da\u011f\u0131l\u0131m\u0131n\u0131n alan\u0131 yaln\u0131zca pozitif say\u0131lardan olu\u015fur.<\/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-f543506f97e1f9c5a56ccc4566a3febf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Gama da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131, \u015fekil parametresi ile \u00f6l\u00e7ek parametresi aras\u0131ndaki orana, yani \u03b1\/\u03bb&#8217;ya 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-326373413d0fe34ef96959dabe9c5cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha}{\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"78\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Gama da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131, \u015fekil parametresinin \u00f6l\u00e7ek parametresinin karesine b\u00f6l\u00fcnmesine 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-693a549de92268ac21add32944199974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{\\alpha}{\\lambda^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> \u03b1&#8217;n\u0131n 1&#8217;den k\u00fc\u00e7\u00fck de\u011ferleri i\u00e7in mod 0&#8217;d\u0131r. Ancak \u03b1 1&#8217;e e\u015fit veya 1&#8217;den b\u00fcy\u00fckse gama da\u011f\u0131l\u0131m\u0131n\u0131n modu a\u015fa\u011f\u0131daki form\u00fclle 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-c9e2762af62f9c38870902ec0284ee07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Mo=0 \\qquad \\text{para } \\alpha<1\\\\[2ex]Mo=\\cfrac{\\alpha-1}{\\lambda} \\qquad \\text{para } \\alpha\\geq1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"214\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Gama da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonu form\u00fcl\u00fc \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-41689ffee11808eab10064a7f3a77693_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{\\lambda(\\lambda x)^{\\alpha-1}e^{-\\lambda x}}{\\Gamma(\\alpha)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"168\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Burada \u0393 \u015fu \u015fekilde tan\u0131mlanan gama fonksiyonudur:<\/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-6e244faebd1174cb6a56e4254bdaaec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Gamma(\\alpha)=\\int_0^\\infty t^{\\alpha-1}e^{-t}dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"169\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> Gama da\u011f\u0131l\u0131m\u0131yla tan\u0131mlanan bir rastgele de\u011fi\u015fkenin k\u00fcm\u00fclatif da\u011f\u0131l\u0131m\u0131n\u0131n form\u00fcl\u00fc 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-6bc3247a247daec5048c409319dc3943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle F(x)=\\int_0^x\\frac{\\lambda(\\lambda y)^{\\alpha-1}e^{-\\lambda y}}{\\Gamma(\\alpha)}\\;dy\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"224\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> \u015eekil parametresi \u03b1 1&#8217;e e\u015fitse, gama da\u011f\u0131l\u0131m\u0131 ayn\u0131 \u00f6l\u00e7ek parametresi \u03bb ile \u00fcstel bir da\u011f\u0131l\u0131ma 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-60ed376f92f0db2c22e19f85bb76f828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\Gamma(1,\\lambda) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\text{Exp}(\\lambda)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u00d6l\u00e7ek parametresi \u03bb bir ortalama oldu\u011funda, gama da\u011f\u0131l\u0131m\u0131 <a href=\"https:\/\/statorials.org\/tr\/ki-kare-dagilimi\/\">ki-kare da\u011f\u0131l\u0131m\u0131n\u0131n<\/a> \u00f6zel bir durumudur.<\/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-efb733464c432d7d1b22ed7e5c534979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle X\\sim \\Gamma\\left(\\frac{n}{2},\\frac{1}{2}\\right) \\text{con } n\\in \\mathbb{N}\\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim \\chi_n^2\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"389\" style=\"vertical-align: -17px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede gama da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece gama da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131, \u00f6zelliklerini ve grafik g\u00f6steriminin nas\u0131l g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc bulacaks\u0131n\u0131z. Gama da\u011f\u0131l\u0131m\u0131 nedir? Gama da\u011f\u0131l\u0131m\u0131, iki karakteristik parametre olan \u03b1 ve \u03bb ile tan\u0131mlanan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Ba\u015fka bir deyi\u015fle, gama da\u011f\u0131l\u0131m\u0131 iki parametresinin de\u011ferine ba\u011fl\u0131d\u0131r: \u03b1 \u015fekil parametresidir ve \u03bb \u00f6l\u00e7ek [&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-225","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 Gama da\u011f\u0131l\u0131m\u0131<\/title>\n<meta name=\"description\" content=\"Burada gama da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011funu, ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131, grafi\u011fini ve gama da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerini bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, 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