{"id":1500,"date":"2023-07-26T03:27:18","date_gmt":"2023-07-26T03:27:18","guid":{"rendered":"https:\/\/statorials.org\/tr\/poisson-guven-araligi\/"},"modified":"2023-07-26T03:27:18","modified_gmt":"2023-07-26T03:27:18","slug":"poisson-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/poisson-guven-araligi\/","title":{"rendered":"Poisson g\u00fcven aral\u0131\u011f\u0131 nas\u0131l hesaplan\u0131r (ad\u0131m ad\u0131m)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/balik-dagitimi\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131,<\/a><\/span> <span style=\"color: #000000;\">olaylar\u0131n ba\u011f\u0131ms\u0131z olarak ve sabit bir ortalama h\u0131zla meydana geldi\u011fi bilindi\u011finde, sabit bir zaman aral\u0131\u011f\u0131nda meydana gelen belirli say\u0131da olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 modellemek i\u00e7in kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir Poisson s\u00fcrecinin ortalama olu\u015fum say\u0131s\u0131n\u0131 bilmek yararl\u0131 olsa da, ortalama olu\u015fum say\u0131s\u0131 etraf\u0131nda bir <a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener\">g\u00fcven aral\u0131\u011f\u0131na<\/a> sahip olmak daha da yararl\u0131 olabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin rastgele bir g\u00fcnde bir \u00e7a\u011fr\u0131 merkezinde veri toplad\u0131\u011f\u0131m\u0131z\u0131 ve saat ba\u015f\u0131na ortalama \u00e7a\u011fr\u0131 say\u0131s\u0131n\u0131n 15 oldu\u011funu g\u00f6relim.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yaln\u0131zca tek bir g\u00fcne ait verileri toplad\u0131\u011f\u0131m\u0131z i\u00e7in \u00e7a\u011fr\u0131 merkezinin y\u0131l boyunca saatte ortalama 15 \u00e7a\u011fr\u0131 ald\u0131\u011f\u0131ndan emin olam\u0131yoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ancak saat ba\u015f\u0131na ortalama \u00e7a\u011fr\u0131 say\u0131s\u0131na ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Poisson g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fc<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">G\u00fcven aral\u0131\u011f\u0131 = [0,5*X <sup>2<\/sup> <sub>2N, \u03b1\/2<\/sub> , 0,5*X <sup>2<\/sup> <sub>2(N+1), 1-\u03b1\/2<\/sub> ]<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">X <sup>2<\/sup> : Ki karenin kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\">N: G\u00f6zlemlenen olaylar\u0131n say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03b1: anlaml\u0131l\u0131k d\u00fczeyi<\/span><\/li>\n<\/ul>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ad\u0131m ad\u0131m \u00f6rnek, pratikte %95 Poisson g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>1. Ad\u0131m: g\u00f6zlemlenen olaylar\u0131 say\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir \u00e7a\u011fr\u0131 merkezinde saat ba\u015f\u0131na ortalama \u00e7a\u011fr\u0131 say\u0131s\u0131n\u0131 15 olarak hesaplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Yani <strong>N = 15<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ve %95&#8217;lik bir g\u00fcven aral\u0131\u011f\u0131 hesaplad\u0131\u011f\u0131m\u0131z i\u00e7in a\u015fa\u011f\u0131daki hesaplamalarda <strong>\u03b1 = 0,05&#8217;i<\/strong> kullanaca\u011f\u0131z.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: G\u00fcven aral\u0131\u011f\u0131n\u0131n alt s\u0131n\u0131r\u0131n\u0131 bulun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">G\u00fcven aral\u0131\u011f\u0131n\u0131n alt s\u0131n\u0131r\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Alt s\u0131n\u0131r = 0,5*X <sup>2<\/sup> <sub>2N, \u03b1\/2<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">Alt s\u0131n\u0131r = 0,5*X <sup>2<\/sup> <sub>2(15), 0,975<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">Alt s\u0131n\u0131r = 0,5*X <sup>2<\/sup> <sub>30, 0,975<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">Alt s\u0131n\u0131r = 0,5*16,791<\/span><\/li>\n<li> <span style=\"color: #000000;\">Alt s\u0131n\u0131r = <strong>8,40<\/strong><\/span><\/li>\n<\/ul>\n<p> <em><span style=\"color: #000000;\"><strong>Not:<\/strong> X <sup>2<\/sup> <sub>30, 0,975&#8217;i<\/sub> hesaplamak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/ki-kare-kritik-deger-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">ki-kare kritik de\u011fer hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kulland\u0131k.<\/span><\/em><\/p>\n<h3> <span style=\"color: #000000;\"><strong>3. Ad\u0131m: G\u00fcven aral\u0131\u011f\u0131n\u0131n \u00fcst s\u0131n\u0131r\u0131n\u0131 bulun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">G\u00fcven aral\u0131\u011f\u0131n\u0131n \u00fcst s\u0131n\u0131r\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00dcst s\u0131n\u0131r = 0,5*X <sup>2<\/sup> <sub>2(N+1), 1-\u03b1\/2<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00dcst s\u0131n\u0131r = 0,5*X <sup>2<\/sup> <sub>2(15+1), 0,025<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00dcst s\u0131n\u0131r = 0,5*X <sup>2<\/sup> <sub>32, 0,025<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00dcst s\u0131n\u0131r = 0,5*49,48<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00dcst s\u0131n\u0131r = <strong>24,74<\/strong><\/span><\/li>\n<\/ul>\n<p> <em><span style=\"color: #000000;\"><strong>Not:<\/strong> X <sup>2<\/sup> <sub>32.0.025&#8217;i<\/sub> hesaplamak i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/ki-kare-kritik-deger-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">ki-kare kritik de\u011fer hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kulland\u0131k.<\/span><\/em><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: G\u00fcven Aral\u0131\u011f\u0131n\u0131 Bulun<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha \u00f6nce hesaplanan alt ve \u00fcst limitleri kullanarak %95 Poisson g\u00fcven aral\u0131\u011f\u0131m\u0131z \u015fu \u015fekilde ortaya \u00e7\u0131k\u0131yor:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">%95 GA = <strong>[8,40, 24,74]<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu, \u00e7a\u011fr\u0131 merkezinin saat ba\u015f\u0131na ald\u0131\u011f\u0131 ger\u00e7ek ortalama \u00e7a\u011fr\u0131 say\u0131s\u0131n\u0131n 8,40 \u00e7a\u011fr\u0131 ile 24,74 \u00e7a\u011fr\u0131 aras\u0131nda oldu\u011fundan %95 emin oldu\u011fumuz anlam\u0131na geliyor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><b>Bonus: Bal\u0131k G\u00fcven Aral\u0131\u011f\u0131 Hesaplay\u0131c\u0131s\u0131<\/b><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poisson g\u00fcven aral\u0131\u011f\u0131n\u0131 otomatik olarak hesaplamak i\u00e7in bu Poisson g\u00fcven aral\u0131\u011f\u0131 hesaplay\u0131c\u0131s\u0131n\u0131 kullanmaktan \u00e7ekinmeyin.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, az \u00f6nce manuel olarak hesaplad\u0131\u011f\u0131m\u0131z Poisson g\u00fcven aral\u0131\u011f\u0131n\u0131 bulmak i\u00e7in bu hesap makinesini nas\u0131l kullanaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14900 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poissonci1.png\" alt=\"Poisson g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplama \u00f6rne\u011fi\" width=\"347\" height=\"282\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Sonu\u00e7lar\u0131n manuel olarak hesaplad\u0131\u011f\u0131m\u0131z g\u00fcven aral\u0131\u011f\u0131na kar\u015f\u0131l\u0131k geldi\u011fini unutmay\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Poisson da\u011f\u0131l\u0131m\u0131, olaylar\u0131n ba\u011f\u0131ms\u0131z olarak ve sabit bir ortalama h\u0131zla meydana geldi\u011fi bilindi\u011finde, sabit bir zaman aral\u0131\u011f\u0131nda meydana gelen belirli say\u0131da olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 modellemek i\u00e7in kullan\u0131lan bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. Bir Poisson s\u00fcrecinin ortalama olu\u015fum say\u0131s\u0131n\u0131 bilmek yararl\u0131 olsa da, ortalama olu\u015fum say\u0131s\u0131 etraf\u0131nda bir g\u00fcven aral\u0131\u011f\u0131na sahip olmak daha da yararl\u0131 olabilir. \u00d6rne\u011fin rastgele bir [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1500","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Poisson G\u00fcven Aral\u0131\u011f\u0131 Nas\u0131l Hesaplan\u0131r (Ad\u0131m Ad\u0131m)<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, ad\u0131m ad\u0131m bir \u00f6rnekle Poisson g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l 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