Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131,<\/strong> bir rastgele de\u011fi\u015fkenin<\/a> her de\u011ferinin ortaya \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan bir fonksiyondur. Basit\u00e7e s\u00f6ylemek gerekirse olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131, rastgele bir deneyin t\u00fcm olas\u0131 sonu\u00e7lar\u0131n\u0131n olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlayan matematiksel bir fonksiyondur.<\/p>\n \u00d6rne\u011fin, izin ver<\/p>\n Bu nedenle olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131, bir \u00f6rnek uzaydaki<\/a> farkl\u0131 olaylar\u0131n olas\u0131l\u0131klar\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131ld\u0131klar\u0131 i\u00e7in olas\u0131l\u0131k teorisinde ve istatistikte s\u0131kl\u0131kla kullan\u0131l\u0131r. <\/p>\n Olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 iki geni\u015f t\u00fcre ayr\u0131labilir: kesikli da\u011f\u0131l\u0131mlar ve s\u00fcrekli da\u011f\u0131l\u0131mlar.<\/p>\n Ayr\u0131k bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131,<\/strong> ayr\u0131 bir rastgele de\u011fi\u015fkenin olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlayan da\u011f\u0131l\u0131md\u0131r. Bu nedenle ayr\u0131k bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 yaln\u0131zca sonlu say\u0131da de\u011fer (genellikle tamsay\u0131 de\u011ferler) alabilir. <\/p>\n Ayr\u0131k tekd\u00fcze da\u011f\u0131l\u0131m,<\/strong> t\u00fcm de\u011ferlerin e\u015f olas\u0131l\u0131kl\u0131 oldu\u011fu, yani ayr\u0131k bir tekd\u00fcze da\u011f\u0131l\u0131mda t\u00fcm de\u011ferlerin ayn\u0131 olu\u015fma olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu ayr\u0131 bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n \u00d6rne\u011fin, t\u00fcm olas\u0131 sonu\u00e7lar\u0131n (1, 2, 3, 4, 5 veya 6) ayn\u0131 olu\u015fma olas\u0131l\u0131\u011f\u0131na sahip olmas\u0131 nedeniyle, bir zar\u0131n at\u0131lmas\u0131 ayr\u0131k ve d\u00fczg\u00fcn bir da\u011f\u0131l\u0131mla tan\u0131mlanabilir.<\/p>\n Genel olarak, ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131m, da\u011f\u0131l\u0131m\u0131n alabilece\u011fi olas\u0131 de\u011ferlerin aral\u0131\u011f\u0131n\u0131 tan\u0131mlayan a<\/em> ve b<\/em> olmak \u00fczere iki karakteristik parametreye sahiptir. Bu nedenle, bir de\u011fi\u015fken ayr\u0131k bir d\u00fczg\u00fcn da\u011f\u0131l\u0131mla tan\u0131mland\u0131\u011f\u0131nda, D\u00fczg\u00fcn(a,b)<\/em> olarak yaz\u0131l\u0131r.<\/p>\n<\/p>\n Ayr\u0131k tekd\u00fcze da\u011f\u0131l\u0131m, rastgele deneyleri tan\u0131mlamak i\u00e7in kullan\u0131labilir \u00e7\u00fcnk\u00fc t\u00fcm sonu\u00e7lar\u0131n ayn\u0131 olas\u0131l\u0131\u011fa sahip olmas\u0131, deneyin rastgele oldu\u011fu anlam\u0131na gelir. <\/p>\n \u0130kili da\u011f\u0131l\u0131m<\/strong> olarak da bilinen Bernoulli da\u011f\u0131l\u0131m\u0131<\/strong> , yaln\u0131zca iki sonuca sahip olabilen ayr\u0131 bir de\u011fi\u015fkeni temsil eden bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r: “ba\u015far\u0131” veya “ba\u015far\u0131s\u0131zl\u0131k”.<\/p>\n Bernoulli da\u011f\u0131l\u0131m\u0131nda “ba\u015far\u0131” bekledi\u011fimiz sonu\u00e7tur ve 1 de\u011ferine sahipken, “ba\u015far\u0131s\u0131zl\u0131k” sonucu beklenenin d\u0131\u015f\u0131nda bir sonu\u00e7tur ve 0 de\u011ferine sahiptir. ba\u015far\u0131\u201d p<\/em> , \u201cba\u015far\u0131s\u0131zl\u0131k\u201d sonucunun olas\u0131l\u0131\u011f\u0131 q=1-p’dir<\/em> .<\/p>\n<\/p>\n Bernoulli da\u011f\u0131l\u0131m\u0131 ismini \u0130svi\u00e7reli istatistik\u00e7i Jacob Bernoulli’den alm\u0131\u015ft\u0131r.<\/p>\n \u0130statistikte, Bernoulli da\u011f\u0131l\u0131m\u0131n\u0131n esas olarak tek bir uygulamas\u0131 vard\u0131r: yaln\u0131zca iki olas\u0131 sonucun (ba\u015far\u0131 ve ba\u015far\u0131s\u0131zl\u0131k) oldu\u011fu deneylerin olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlamak. Dolay\u0131s\u0131yla Bernoulli da\u011f\u0131l\u0131m\u0131n\u0131 kullanan bir deneye Bernoulli testi veya Bernoulli deneyi denir. <\/p>\n Binom<\/strong> da\u011f\u0131l\u0131m\u0131 olarak da adland\u0131r\u0131lan binom da\u011f\u0131l\u0131m\u0131<\/strong> , sabit bir ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 ile bir dizi ba\u011f\u0131ms\u0131z, ikili deney ger\u00e7ekle\u015ftirirken elde edilen ba\u015far\u0131lar\u0131n say\u0131s\u0131n\u0131 sayan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Ba\u015fka bir deyi\u015fle binom da\u011f\u0131l\u0131m\u0131, bir dizi Bernoulli denemesinin ba\u015far\u0131l\u0131 sonu\u00e7lar\u0131n\u0131n say\u0131s\u0131n\u0131 tan\u0131mlayan bir da\u011f\u0131l\u0131md\u0131r.<\/p>\n \u00d6rne\u011fin, bir paran\u0131n 25 kez at\u0131lmas\u0131 s\u0131ras\u0131nda ortaya \u00e7\u0131kan “tura” say\u0131s\u0131 binom da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n Genel olarak ger\u00e7ekle\u015ftirilen deneylerin toplam say\u0131s\u0131 n<\/em> parametresi ile tan\u0131mlan\u0131rken, p<\/em> her deneyin ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131d\u0131r. B\u00f6ylece, binom da\u011f\u0131l\u0131m\u0131n\u0131 takip eden bir rastgele de\u011fi\u015fken \u015fu \u015fekilde yaz\u0131l\u0131r:<\/p>\n<\/p>\n Binom da\u011f\u0131l\u0131m\u0131nda ayn\u0131 deneyin n<\/em> kez tekrarland\u0131\u011f\u0131n\u0131 ve deneylerin birbirinden ba\u011f\u0131ms\u0131z oldu\u011funu, dolay\u0131s\u0131yla her deneyin ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n ayn\u0131 oldu\u011funu (p)<\/em> unutmay\u0131n. <\/p>\n Poisson da\u011f\u0131l\u0131m\u0131,<\/strong> belirli bir s\u00fcre boyunca belirli say\u0131da olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Ba\u015fka bir deyi\u015fle Poisson da\u011f\u0131l\u0131m\u0131, bir olgunun belirli bir zaman aral\u0131\u011f\u0131nda tekrarlanma say\u0131s\u0131n\u0131 tan\u0131mlayan rastgele de\u011fi\u015fkenleri modellemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n \u00d6rne\u011fin, bir telefon santralinin dakika ba\u015f\u0131na ald\u0131\u011f\u0131 \u00e7a\u011fr\u0131 say\u0131s\u0131, Poisson da\u011f\u0131l\u0131m\u0131 kullan\u0131larak tan\u0131mlanabilen ayr\u0131 bir rastgele de\u011fi\u015fkendir.<\/p>\n Poisson da\u011f\u0131l\u0131m\u0131n\u0131n, Yunanca \u03bb harfiyle temsil edilen karakteristik bir parametresi vard\u0131r ve incelenen olay\u0131n belirli bir aral\u0131kta ka\u00e7 kez meydana gelmesinin beklendi\u011fini g\u00f6sterir. <\/p>\n<\/p>\n \u00c7ok terimli da\u011f\u0131l\u0131m<\/strong> (veya \u00e7ok terimli da\u011f\u0131l\u0131m<\/strong> ), birbirini d\u0131\u015flayan birka\u00e7 olay\u0131n birka\u00e7 denemeden sonra belirli say\u0131da meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlayan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n Yani, rastgele bir deney \u00fc\u00e7 veya daha fazla \u00f6zel olayla sonu\u00e7lanabiliyorsa ve her olay\u0131n ayr\u0131 ayr\u0131 meydana gelme olas\u0131l\u0131\u011f\u0131 biliniyorsa, \u00e7ok terimli da\u011f\u0131l\u0131m, birden fazla deney ger\u00e7ekle\u015ftirildi\u011finde belirli say\u0131da olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r. her zaman.<\/p>\n Dolay\u0131s\u0131yla \u00e7ok terimli da\u011f\u0131l\u0131m, binom da\u011f\u0131l\u0131m\u0131n\u0131n bir genellemesidir. <\/p>\n Geometrik da\u011f\u0131l\u0131m,<\/strong> ilk ba\u015far\u0131l\u0131 sonucu elde etmek i\u00e7in gereken Bernoulli denemelerinin say\u0131s\u0131n\u0131 tan\u0131mlayan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Yani, Bernoulli deneylerinden biri pozitif sonu\u00e7 elde edene kadar tekrarlanan s\u00fcre\u00e7lerin geometrik da\u011f\u0131l\u0131m modelleri.<\/p>\n \u00d6rne\u011fin otoyolda sar\u0131 bir araba g\u00f6rene kadar ge\u00e7en araba say\u0131s\u0131 geometrik bir da\u011f\u0131l\u0131md\u0131r.<\/p>\n Bernoulli testinin iki olas\u0131 sonucu olan bir deney oldu\u011funu unutmay\u0131n: “ba\u015far\u0131” ve “ba\u015far\u0131s\u0131zl\u0131k”. Yani \u201cba\u015far\u0131\u201d olas\u0131l\u0131\u011f\u0131 p<\/em> ise, \u201cba\u015far\u0131s\u0131zl\u0131k\u201d olas\u0131l\u0131\u011f\u0131 q=1-p’dir<\/em> .<\/p>\n Bu nedenle geometrik da\u011f\u0131l\u0131m, ger\u00e7ekle\u015ftirilen t\u00fcm deneylerin ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 olan p<\/em> parametresine ba\u011fl\u0131d\u0131r. Ayr\u0131ca p<\/em> olas\u0131l\u0131\u011f\u0131 t\u00fcm deneyler i\u00e7in ayn\u0131d\u0131r. <\/p>\n<\/p>\n Negatif binom da\u011f\u0131l\u0131m\u0131,<\/strong> belirli say\u0131da pozitif sonu\u00e7 elde etmek i\u00e7in gereken Bernoulli denemelerinin say\u0131s\u0131n\u0131 tan\u0131mlayan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n Bu nedenle, negatif bir binom da\u011f\u0131l\u0131m\u0131n\u0131n iki karakteristik parametresi vard\u0131r: r<\/em> , istenen ba\u015far\u0131l\u0131 sonu\u00e7lar\u0131n say\u0131s\u0131d\u0131r ve p<\/em> , ger\u00e7ekle\u015ftirilen her Bernoulli deneyinin ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131d\u0131r.<\/p>\n<\/p>\n Dolay\u0131s\u0131yla negatif binom da\u011f\u0131l\u0131m\u0131, pozitif sonu\u00e7lar<\/em> elde etmek i\u00e7in gerekti\u011fi kadar Bernoulli denemesinin yap\u0131ld\u0131\u011f\u0131 bir s\u00fcreci tan\u0131mlar. Ayr\u0131ca, t\u00fcm bu Bernoulli denemeleri ba\u011f\u0131ms\u0131zd\u0131r ve sabit bir ba\u015far\u0131<\/em> olas\u0131l\u0131\u011f\u0131na sahiptir.<\/p>\n \u00d6rne\u011fin, negatif binom da\u011f\u0131l\u0131m\u0131n\u0131 takip eden rastgele bir de\u011fi\u015fken, 6 say\u0131s\u0131 \u00fc\u00e7 kez at\u0131lana kadar bir zar\u0131n ka\u00e7 kez at\u0131lmas\u0131 gerekti\u011fidir. <\/p>\n Hipergeometrik da\u011f\u0131l\u0131m,<\/strong> bir pop\u00fclasyondan n<\/em> \u00f6\u011fenin de\u011fi\u015ftirilmesi gerekmeden rastgele bir \u00e7\u0131karma i\u015flemindeki ba\u015far\u0131l\u0131 vakalar\u0131n say\u0131s\u0131n\u0131 tan\u0131mlayan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n Yani hipergeometrik da\u011f\u0131l\u0131m, bir pop\u00fclasyondan herhangi birini de\u011fi\u015ftirmeden n<\/em> \u00f6\u011fe \u00e7\u0131kar\u0131rken x<\/em> ba\u015far\u0131 elde etme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/p>\n Bu nedenle hipergeometrik da\u011f\u0131l\u0131m\u0131n \u00fc\u00e7 parametresi vard\u0131r:<\/p>\n S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131,<\/strong> ondal\u0131k de\u011ferler de dahil olmak \u00fczere bir aral\u0131ktaki herhangi bir de\u011feri alabilen da\u011f\u0131l\u0131md\u0131r. Bu nedenle s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131, s\u00fcrekli bir rastgele de\u011fi\u015fkenin olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlar. <\/p>\n Dikd\u00f6rtgen<\/strong> da\u011f\u0131l\u0131m olarak da adland\u0131r\u0131lan s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m<\/strong> , t\u00fcm de\u011ferlerin ayn\u0131 g\u00f6r\u00fcnme olas\u0131l\u0131\u011f\u0131na sahip oldu\u011fu bir s\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 t\u00fcr\u00fcd\u00fcr. Ba\u015fka bir deyi\u015fle s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m, olas\u0131l\u0131\u011f\u0131n belirli bir aral\u0131kta d\u00fczg\u00fcn da\u011f\u0131ld\u0131\u011f\u0131 bir da\u011f\u0131l\u0131md\u0131r.<\/p>\n S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m, sabit olas\u0131l\u0131\u011fa sahip s\u00fcrekli de\u011fi\u015fkenleri tan\u0131mlamak i\u00e7in kullan\u0131l\u0131r. Benzer \u015fekilde, rastgele s\u00fcre\u00e7leri tan\u0131mlamak i\u00e7in s\u00fcrekli tekd\u00fcze da\u011f\u0131l\u0131m kullan\u0131l\u0131r, \u00e7\u00fcnk\u00fc t\u00fcm sonu\u00e7lar\u0131n ayn\u0131 olas\u0131l\u0131\u011fa sahip olmas\u0131, sonu\u00e7ta rastgelelik oldu\u011fu anlam\u0131na gelir.<\/p>\n S\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m, e\u015f olas\u0131l\u0131k aral\u0131\u011f\u0131n\u0131 tan\u0131mlayan a<\/em> ve b<\/em> olmak \u00fczere iki karakteristik parametreye sahiptir. Dolay\u0131s\u0131yla s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m\u0131n sembol\u00fc U(a,b)’<\/em> dir; burada a<\/em> ve b<\/em> , da\u011f\u0131l\u0131m\u0131n karakteristik de\u011ferleridir.<\/p>\n<\/p>\n \u00d6rne\u011fin, rastgele bir deneyin sonucu 5 ile 9 aras\u0131nda herhangi bir de\u011fer alabiliyorsa ve olas\u0131 t\u00fcm sonu\u00e7lar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 ayn\u0131ysa, deney s\u00fcrekli d\u00fczg\u00fcn da\u011f\u0131l\u0131m U(5.9) ile sim\u00fcle edilebilir. <\/p>\n Normal da\u011f\u0131l\u0131m,<\/strong> grafi\u011fi \u00e7an \u015feklinde ve ortalamas\u0131na g\u00f6re simetrik olan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. \u0130statistikte normal da\u011f\u0131l\u0131m \u00e7ok farkl\u0131 \u00f6zelliklere sahip olgular\u0131 modellemek i\u00e7in kullan\u0131l\u0131r, bu nedenle bu da\u011f\u0131l\u0131m \u00e7ok \u00f6nemlidir.<\/p>\n Asl\u0131nda istatistikte normal da\u011f\u0131l\u0131m, t\u00fcm olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 aras\u0131nda a\u00e7\u0131k ara en \u00f6nemli da\u011f\u0131l\u0131m olarak kabul edilir, \u00e7\u00fcnk\u00fc sadece \u00e7ok say\u0131da ger\u00e7ek d\u00fcnya olay\u0131n\u0131 modellemekle kalmaz, ayn\u0131 zamanda normal da\u011f\u0131l\u0131m di\u011fer olas\u0131l\u0131k t\u00fcrlerine yakla\u015f\u0131k olarak da kullan\u0131labilir. da\u011f\u0131t\u0131mlar. belirli ko\u015fullar alt\u0131nda.<\/p>\n Normal da\u011f\u0131l\u0131m\u0131n sembol\u00fc b\u00fcy\u00fck harf N’dir. Yani bir de\u011fi\u015fkenin normal da\u011f\u0131l\u0131m izledi\u011fini belirtmek i\u00e7in N harfi ile g\u00f6sterilir ve parantez i\u00e7inde aritmetik ortalamas\u0131 ve standart sapmas\u0131 de\u011ferleri eklenir.<\/p>\n<\/p>\n Normal da\u011f\u0131l\u0131m\u0131n Gauss da\u011f\u0131l\u0131m\u0131<\/strong> , Gauss da\u011f\u0131l\u0131m\u0131<\/strong> ve Laplace-Gauss da\u011f\u0131l\u0131m\u0131<\/strong> dahil olmak \u00fczere bir\u00e7ok farkl\u0131 ad\u0131 vard\u0131r. <\/p>\n Lognormal da\u011f\u0131l\u0131m<\/strong> veya lognormal da\u011f\u0131l\u0131m<\/strong> , logaritmas\u0131 normal da\u011f\u0131l\u0131ma uyan rastgele bir de\u011fi\u015fkeni tan\u0131mlayan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n Bu nedenle, e\u011fer X de\u011fi\u015fkeni normal da\u011f\u0131l\u0131ma sahipse, \u00fcstel fonksiyon e x<\/sup> lognormal da\u011f\u0131l\u0131ma sahiptir.<\/p>\n<\/p>\n Logaritman\u0131n yaln\u0131zca bir pozitif arg\u00fcman\u0131 kabul eden bir fonksiyon olmas\u0131 nedeniyle lognormal da\u011f\u0131l\u0131m\u0131n yaln\u0131zca de\u011fi\u015fkenin de\u011ferleri pozitif oldu\u011funda kullan\u0131labilece\u011fini unutmay\u0131n.<\/p>\n Lognormal da\u011f\u0131l\u0131m\u0131n istatistikteki farkl\u0131 uygulamalar\u0131 aras\u0131nda, bu da\u011f\u0131l\u0131m\u0131n finansal yat\u0131r\u0131mlar\u0131 analiz etmek ve g\u00fcvenilirlik analizleri yapmak i\u00e7in kullan\u0131lmas\u0131n\u0131 \u00f6ne \u00e7\u0131kar\u0131yoruz.<\/p>\n Lognormal da\u011f\u0131l\u0131m ayn\u0131 zamanda Tinaut da\u011f\u0131l\u0131m\u0131 olarak<\/strong> da bilinir ve bazen lognormal da\u011f\u0131l\u0131m<\/strong> veya log-normal da\u011f\u0131l\u0131m<\/strong> olarak da yaz\u0131l\u0131r. <\/p>\n 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 k<\/em> ba\u011f\u0131ms\u0131z rastgele de\u011fi\u015fkenin karelerinin toplam\u0131d\u0131r.<\/p>\n Dolay\u0131s\u0131yla Ki-kare da\u011f\u0131l\u0131m\u0131 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 Ki-kare da\u011f\u0131l\u0131m\u0131 Pearson da\u011f\u0131l\u0131m\u0131<\/strong> olarak da bilinir.<\/p>\n 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 \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131<\/strong> istatistikte yayg\u0131n olarak kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. \u00d6zellikle, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131, iki numunenin ortalamalar\u0131 aras\u0131ndaki fark\u0131 belirlemek ve g\u00fcven aral\u0131klar\u0131n\u0131 olu\u015fturmak i\u00e7in \u00d6\u011frenci t testinde kullan\u0131l\u0131r.<\/p>\n \u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131, istatistik\u00e7i William Sealy Gosset taraf\u0131ndan 1908 y\u0131l\u0131nda “\u00d6\u011frenci” takma ad\u0131 alt\u0131nda geli\u015ftirildi.<\/p>\n \u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131, toplam g\u00f6zlem say\u0131s\u0131ndan bir birimin \u00e7\u0131kar\u0131lmas\u0131yla elde edilen serbestlik derecesi say\u0131s\u0131yla tan\u0131mlan\u0131r. Bu nedenle, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik derecesini belirleme form\u00fcl\u00fc \u03bd=n-1’dir<\/em> . <\/p>\n<\/p>\n Fisher-Snedecor<\/strong> F da\u011f\u0131l\u0131m\u0131<\/strong> veya basit\u00e7e F da\u011f\u0131l\u0131m\u0131<\/strong> olarak da adland\u0131r\u0131lan Snedecor F da\u011f\u0131l\u0131m\u0131, istatistiksel \u00e7\u0131kar\u0131mda, \u00f6zellikle varyans analizinde kullan\u0131lan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n Snedecor F da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerinden biri, serbestlik derecesini g\u00f6steren m<\/em> ve n<\/em> olmak \u00fczere iki ger\u00e7ek parametrenin de\u011feriyle tan\u0131mlanmas\u0131d\u0131r. Dolay\u0131s\u0131yla Snedecor da\u011f\u0131l\u0131m\u0131 F’nin sembol\u00fc Fm ,n’dir<\/sub><\/em> ; burada m<\/em> ve n<\/em> , da\u011f\u0131l\u0131m\u0131 tan\u0131mlayan parametrelerdir.<\/p>\n<\/p>\n Matematiksel olarak Snedecor F da\u011f\u0131l\u0131m\u0131, bir ki-kare da\u011f\u0131l\u0131m\u0131 ile onun serbestlik dereceleri aras\u0131ndaki b\u00f6l\u00fcm\u00fcn, ba\u015fka bir ki-kare da\u011f\u0131l\u0131m\u0131 ile onun serbestlik dereceleri aras\u0131ndaki b\u00f6l\u00fcme b\u00f6l\u00fcnmesine e\u015fittir. B\u00f6ylece Snedecor F da\u011f\u0131l\u0131m\u0131n\u0131 tan\u0131mlayan form\u00fcl a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n Fisher-Snedecor F da\u011f\u0131l\u0131m\u0131, ad\u0131n\u0131 \u0130ngiliz istatistik\u00e7i Ronald Fisher ve Amerikal\u0131 istatistik\u00e7i George Snedecor’dan almaktad\u0131r.<\/p>\n \u0130statistikte Fisher-Snedecor F da\u011f\u0131l\u0131m\u0131n\u0131n farkl\u0131 uygulamalar\u0131 vard\u0131r. \u00d6rne\u011fin, Fisher-Snedecor F da\u011f\u0131l\u0131m\u0131 farkl\u0131 do\u011frusal regresyon modellerini kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r ve bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131, varyans analizinde (ANOVA) kullan\u0131l\u0131r. <\/p>\n \u00dcstel da\u011f\u0131l\u0131m,<\/strong> rastgele bir olay\u0131n meydana gelmesi i\u00e7in bekleme s\u00fcresini modellemek i\u00e7in kullan\u0131lan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n Daha do\u011frusu \u00fcstel da\u011f\u0131l\u0131m, Poisson da\u011f\u0131l\u0131m\u0131n\u0131 takip eden iki olay aras\u0131ndaki bekleme s\u00fcresini tan\u0131mlamay\u0131 m\u00fcmk\u00fcn k\u0131lar. Bu nedenle \u00fcstel da\u011f\u0131l\u0131m Poisson da\u011f\u0131l\u0131m\u0131yla yak\u0131ndan ili\u015fkilidir.<\/p>\n \u00dcstel da\u011f\u0131l\u0131m, Yunan harfi \u03bb ile temsil edilen karakteristik bir parametreye sahiptir ve incelenen olay\u0131n belirli bir s\u00fcre i\u00e7inde ka\u00e7 kez meydana gelmesinin beklendi\u011fini g\u00f6sterir.<\/p>\n<\/p>\n Benzer \u015fekilde \u00fcstel da\u011f\u0131l\u0131m da bir ar\u0131za meydana gelene kadar ge\u00e7en s\u00fcreyi modellemek i\u00e7in kullan\u0131l\u0131r. Bu nedenle \u00fcstel da\u011f\u0131l\u0131m\u0131n g\u00fcvenilirlik ve hayatta kalma teorisinde \u00e7e\u015fitli uygulamalar\u0131 vard\u0131r. <\/p>\n<\/span> Olas\u0131l\u0131k da\u011f\u0131l\u0131m t\u00fcrleri<\/span><\/h2>\n
\n
<\/span> Ayr\u0131k olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131<\/span><\/h3>\n
<\/span> Ayr\u0131k d\u00fczg\u00fcn da\u011f\u0131l\u0131m<\/span><\/h4>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9977cf21c766a3d0ee2d79c8210dc598_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Bernoulli da\u011f\u0131l\u0131m\u0131<\/span><\/h4>\n
![\"\\begin{array}{c}X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-384fd7d96d4d6584739b04a6e331b251_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Binom da\u011f\u0131l\u0131m\u0131<\/span><\/h4>\n
![\"X\\sim\\text{Bin}(n,p)\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2f2b2be5bfe6c63bd13c552f4c893f59_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span>Bal\u0131k da\u011f\u0131t\u0131m\u0131<\/span><\/h4>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-be6e10a2b0137ec81fc7d366f237d1b2_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> \u00e7ok terimli da\u011f\u0131l\u0131m<\/span><\/h4>\n
<\/span>geometrik da\u011f\u0131l\u0131m<\/span><\/h4>\n
![\"X\\sim\\text{Geom\\'etrica}(p)\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-22fef9b6ab8e3b351598caf9925c2b3f_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> negatif binom da\u011f\u0131l\u0131m\u0131<\/span><\/h4>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-171122de529a1c006bc46e8d89176016_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> hipergeometrik da\u011f\u0131l\u0131m<\/span><\/h4>\n
\n
![\"X](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bd43d7c14739c66e63b224abf6cc20b3_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131<\/span><\/h3>\n
<\/span> d\u00fczg\u00fcn ve s\u00fcrekli da\u011f\u0131t\u0131m<\/span><\/h4>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-339036da3788f71282d3936dd092730c_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span>Normal da\u011f\u0131l\u0131m<\/span><\/h4>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9e682e473c45274794b6fece4d7683f0_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Lognormal da\u011f\u0131l\u0131m<\/span><\/h4>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-216d8f120f09a37cd8f797bb3b115a40_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Ki-kare da\u011f\u0131l\u0131m\u0131<\/span><\/h4>\n
![\"\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9ea0bf7a87071883ceae5e419bae9e71_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> \u00d6\u011frencinin t da\u011f\u0131l\u0131m\u0131<\/span><\/h4>\n
![\"\\begin{array}{c}\\nu=n-1\\\\[2ex]X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1c805dc2d6ca050feb70dad99de53402_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Snedecor F Da\u011f\u0131t\u0131m\u0131<\/span><\/h4>\n
![\"F_{m,n}\\qquad](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b6126a79c671267450b6523ca16b4a92_l3.png\")
0″ title=”Rendered by QuickLaTeX.com” height=”18″ width=”139″ style=”vertical-align: -6px;”><\/p>\n<\/p>\n![\"\\left.\\begin{array}{c}](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d407869e61ca4357ffbcb40df3bd83ab_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> \u00fcstel da\u011f\u0131l\u0131m<\/span><\/h4>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05fa833356caeb193384f780ae4edac1_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
![\"\\begin{array}{c}X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ee1d0d8a1624a017b8ef9ce8a67c694e_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n