S\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131,<\/strong> da\u011f\u0131l\u0131m fonksiyonu<\/a> s\u00fcrekli olan bir 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<\/a> olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlar.<\/p>\n \u00d6rne\u011fin normal da\u011f\u0131l\u0131m ve \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131 s\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131d\u0131r.<\/p>\n S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131n\u0131n \u00f6zelliklerinden biri de belirli bir aral\u0131kta her de\u011feri alabilmesidir. Dolay\u0131s\u0131yla kesikli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131ndan farkl\u0131 olarak s\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 ondal\u0131k de\u011ferler alabilir.<\/p>\n S\u00fcrekli da\u011f\u0131l\u0131mlarda k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in da\u011f\u0131l\u0131m e\u011frisinin alt\u0131ndaki alan\u0131n bulunmas\u0131 gerekir, dolay\u0131s\u0131yla bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131nda k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonu yo\u011funluk fonksiyonunun<\/a> integraline e\u015fde\u011ferdir. <\/p>\n<\/p>\n S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra, kavram\u0131 daha iyi anlamak i\u00e7in bu t\u00fcr da\u011f\u0131l\u0131m\u0131n birka\u00e7 \u00f6rne\u011fini g\u00f6rece\u011fiz.<\/p>\n S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131na \u00f6rnekler:<\/u><\/strong><\/p>\n S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131n\u0131n ana t\u00fcrleri<\/strong> \u015funlard\u0131r:<\/p>\n S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n her t\u00fcr\u00fc a\u015fa\u011f\u0131da ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klanmaktad\u0131r. <\/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 derecelerini 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 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 Bu nedenle de\u011feri 0 ile 1 aras\u0131nda olan s\u00fcrekli rastgele de\u011fi\u015fkenleri tan\u0131mlamak i\u00e7in beta da\u011f\u0131l\u0131m\u0131 kullan\u0131l\u0131r.<\/p>\n 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 \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 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 Gama da\u011f\u0131l\u0131m\u0131n\u0131n sembol\u00fc b\u00fcy\u00fck Yunan harfi \u0393’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 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 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 Weibull da\u011f\u0131l\u0131m\u0131<\/strong> iki karakteristik parametreyle tan\u0131mlanan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r: \u015fekil parametresi \u03b1 ve \u00f6l\u00e7ek parametresi \u03bb.<\/p>\n \u0130statistiklerde Weibull da\u011f\u0131l\u0131m\u0131 esas olarak hayatta kalma analizi i\u00e7in kullan\u0131l\u0131r. Ayn\u0131 \u015fekilde Weibull da\u011f\u0131l\u0131m\u0131n\u0131n da farkl\u0131 alanlarda bir\u00e7ok uygulamas\u0131 vard\u0131r.<\/p>\n<\/p>\n Yazarlara g\u00f6re Weibull da\u011f\u0131l\u0131m\u0131 \u00fc\u00e7 parametreyle de parametrelendirilebilir. Daha sonra da\u011f\u0131l\u0131m grafi\u011finin ba\u015flad\u0131\u011f\u0131 apsisi g\u00f6steren e\u015fik de\u011feri ad\u0131 verilen \u00fc\u00e7\u00fcnc\u00fc bir parametre eklenir.<\/p>\n Weibull da\u011f\u0131l\u0131m\u0131, ad\u0131n\u0131 1951 y\u0131l\u0131nda onu ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klayan \u0130sve\u00e7li Waloddi Weibull’dan alm\u0131\u015ft\u0131r. Ancak Weibull da\u011f\u0131l\u0131m\u0131 1927 y\u0131l\u0131nda Maurice Fr\u00e9chet taraf\u0131ndan ke\u015ffedilmi\u015f ve ilk olarak 1933 y\u0131l\u0131nda Rosin ve Rammler taraf\u0131ndan uygulanm\u0131\u015ft\u0131r. <\/p>\n Pareto da\u011f\u0131l\u0131m\u0131,<\/strong> istatistikte Pareto ilkesini modellemek i\u00e7in kullan\u0131lan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Dolay\u0131s\u0131yla Pareto da\u011f\u0131l\u0131m\u0131, ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 di\u011fer de\u011ferlerden \u00e7ok daha y\u00fcksek olan birka\u00e7 de\u011fere sahip bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n 80-20 kural\u0131 olarak da adland\u0131r\u0131lan Pareto yasas\u0131n\u0131n, bir olgunun nedeninin \u00e7o\u011funun n\u00fcfusun k\u00fc\u00e7\u00fck bir k\u0131sm\u0131ndan kaynakland\u0131\u011f\u0131n\u0131 s\u00f6yleyen istatistiksel bir ilke oldu\u011funu unutmay\u0131n.<\/p>\n Pareto da\u011f\u0131l\u0131m\u0131n\u0131n iki karakteristik parametresi vard\u0131r: \u00f6l\u00e7ek parametresi x m<\/sub> ve \u015fekil parametresi \u03b1.<\/p>\n<\/p>\n Ba\u015flang\u0131\u00e7ta Pareto da\u011f\u0131l\u0131m\u0131, n\u00fcfusun k\u00fc\u00e7\u00fck bir k\u0131sm\u0131ndan kaynakland\u0131\u011f\u0131 i\u00e7in n\u00fcfus i\u00e7indeki zenginlik da\u011f\u0131l\u0131m\u0131n\u0131 tan\u0131mlamak i\u00e7in kullan\u0131l\u0131yordu. Ancak \u015fu anda Pareto da\u011f\u0131l\u0131m\u0131n\u0131n bir\u00e7ok uygulamas\u0131 vard\u0131r; \u00f6rne\u011fin kalite kontrolde, ekonomide, bilimde, sosyal alanda vb. <\/p>\n![\"\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4a24c53cda32a192e8dd8773df5b8ff6_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> S\u00fcrekli Olas\u0131l\u0131k Da\u011f\u0131l\u0131mlar\u0131na \u00d6rnekler<\/span><\/h2>\n
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<\/span> S\u00fcrekli olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131n\u0131n t\u00fcrleri<\/span><\/h2>\n
\n
<\/span> D\u00fczg\u00fcn ve s\u00fcrekli da\u011f\u0131t\u0131m<\/span><\/h3>\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><\/h3>\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><\/h3>\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><\/h3>\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><\/h3>\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><\/h3>\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> \u00dcstel da\u011f\u0131l\u0131m<\/span><\/h3>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05fa833356caeb193384f780ae4edac1_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Beta Da\u011f\u0131l\u0131m\u0131<\/span><\/h3>\n
![\"\\begin{array}{c}X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ee1d0d8a1624a017b8ef9ce8a67c694e_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Gama da\u011f\u0131l\u0131m\u0131<\/span><\/h3>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1b0ab2e724ffd74455d0907b39f4a598_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span>Weibull da\u011f\u0131l\u0131m\u0131<\/span><\/h3>\n
![\"X\\sim\\text{Weibull}(\\alpha,\\lambda)\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-14be9904756b25df209befbae173e29e_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Pareto da\u011f\u0131l\u0131m\u0131<\/span><\/h3>\n
![\"X\\sim](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n