{"id":2556,"date":"2023-07-21T18:20:28","date_gmt":"2023-07-21T18:20:28","guid":{"rendered":"https:\/\/statorials.org\/tr\/balik-ve-normal-dagilim\/"},"modified":"2023-07-21T18:20:28","modified_gmt":"2023-07-21T18:20:28","slug":"balik-ve-normal-dagilim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/balik-ve-normal-dagilim\/","title":{"rendered":"Poisson da\u011f\u0131l\u0131m\u0131 veya normal da\u011f\u0131l\u0131m: fark nedir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Poisson da\u011f\u0131l\u0131m\u0131<\/strong> ve <strong>normal da\u011f\u0131l\u0131m<\/strong> istatistikte en s\u0131k kullan\u0131lan olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131ndan ikisidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde her da\u011f\u0131t\u0131m\u0131n h\u0131zl\u0131 bir a\u00e7\u0131klamas\u0131n\u0131n yan\u0131 s\u0131ra da\u011f\u0131t\u0131mlar aras\u0131ndaki iki \u00f6nemli fark da sunulmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Genel bak\u0131\u015f: Poisson da\u011f\u0131l\u0131m\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Poisson da\u011f\u0131l\u0131m\u0131<\/strong> belirli bir zaman aral\u0131\u011f\u0131nda <em>k<\/em> ba\u015far\u0131 elde etme olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir <em>X<\/em><a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noreferrer noopener\">rastgele de\u011fi\u015fkeni<\/a> bir Poisson da\u011f\u0131l\u0131m\u0131n\u0131 takip ediyorsa, <em>X<\/em> = <em>k<\/em> ba\u015far\u0131s\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fclle bulunabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = \u03bb <sup>k<\/sup> * e <sup>\u2013 \u03bb<\/sup> \/ k!<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03bb:<\/strong> belirli bir aral\u0131kta meydana gelen ortalama ba\u015far\u0131 say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>k:<\/strong> ba\u015far\u0131 say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><b>e:<\/b> yakla\u015f\u0131k 2,71828&#8217;e e\u015fit bir sabit<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir hastanede saatte ortalama 2 do\u011fum ger\u00e7ekle\u015fti\u011fini varsayal\u0131m. Belirli bir saatte 3 do\u011fum ya\u015fanma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in yukar\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=3)<\/strong> = 2 <sup>3<\/sup> * e <sup>\u2013 2\/3<\/sup> ! = <strong>0,1805<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir saatte 3 do\u011fum ya\u015fanma olas\u0131l\u0131\u011f\u0131 <strong>0,1805&#8217;tir<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Genel bak\u0131\u015f: normal da\u011f\u0131l\u0131m<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Normal da\u011f\u0131l\u0131m,<\/strong> bir rastgele de\u011fi\u015fkenin belirli bir aral\u0131kta de\u011fer alma olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Normal bir da\u011f\u0131l\u0131m\u0131n <a href=\"https:\/\/statorials.org\/tr\/cdf-vs-pdf\/\" target=\"_blank\" rel=\"noopener\">olas\u0131l\u0131k yo\u011funluk fonksiyonu<\/a> \u015fu \u015fekilde yaz\u0131labilir:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">P(X=x) = (1\/\u03c3\u221a <span style=\"border-top: 1px solid black;\">2\u03c0<\/span> )e <sup>-1\/2((x-\u03bc)\/\u03c3) <sup>2<\/sup><\/sup><\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03c3:<\/strong> Da\u011f\u0131l\u0131m\u0131n standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc:<\/strong> Da\u011f\u0131l\u0131m\u0131n ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><b>x:<\/b> rastgele de\u011fi\u015fkenin de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir su samuru t\u00fcr\u00fcn\u00fcn a\u011f\u0131rl\u0131\u011f\u0131n\u0131n \u03bc = 40 pound ve \u03c3 = 5 pound ile normal olarak da\u011f\u0131ld\u0131\u011f\u0131n\u0131 varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu pop\u00fclasyondan rastgele bir su samuru se\u00e7ersek, a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 38 ila 42 pound aras\u0131nda olma olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">P<\/span> <span style=\"border-top: 1px solid black;\">(<\/span> <sup><sup>38<\/sup><\/sup> <sup>&lt; \/5) <sup>2<\/sup><\/sup> = <strong>0,3108<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Rastgele se\u00e7ilen su samuru a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 38 ile 42 pound aras\u0131nda olma olas\u0131l\u0131\u011f\u0131 <strong>0,3108&#8217;dir<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Fark #1: Gizli vs. S\u00fcrekli Veri<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poisson da\u011f\u0131l\u0131m\u0131 ile normal da\u011f\u0131l\u0131m aras\u0131ndaki ilk fark, her olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n modelledi\u011fi veri t\u00fcr\u00fcd\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yaln\u0131zca s\u0131f\u0131ra e\u015fit veya s\u0131f\u0131rdan b\u00fcy\u00fck tam say\u0131 de\u011ferleri alabilen <strong>ayr\u0131k verilerle<\/strong> \u00e7al\u0131\u015f\u0131rken <strong>Poisson da\u011f\u0131l\u0131m\u0131<\/strong> kullan\u0131l\u0131r. \u0130\u015fte baz\u0131 \u00f6rnekler:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00c7a\u011fr\u0131 merkezinde saat ba\u015f\u0131na al\u0131nan \u00e7a\u011fr\u0131 say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir restoranda g\u00fcnl\u00fck m\u00fc\u015fteri say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ayl\u0131k trafik kazas\u0131 say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Her senaryoda rastgele de\u011fi\u015fken yaln\u0131zca 0, 1, 2, 3 vb. de\u011ferini alabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Negatif sonsuzdan pozitif sonsuza kadar <em>herhangi bir<\/em> de\u011fer alabilen <strong>s\u00fcrekli verilerle<\/strong> \u00e7al\u0131\u015f\u0131rken <strong>normal da\u011f\u0131l\u0131m<\/strong> kullan\u0131l\u0131r. \u0130\u015fte baz\u0131 \u00f6rnekler:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Belirli bir hayvan\u0131n a\u011f\u0131rl\u0131\u011f\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">Belirli bir bitkinin y\u00fcksekli\u011fi<\/span><\/li>\n<li> <span style=\"color: #000000;\">Kad\u0131nlar\u0131n maraton s\u00fcreleri<\/span><\/li>\n<li> <span style=\"color: #000000;\">Santigrat cinsinden s\u0131cakl\u0131k<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu senaryolarda rastgele de\u011fi\u015fkenler -11,3, 21,343435, 85 vb. gibi <em>herhangi bir<\/em> de\u011feri alabilir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Fark #2: da\u011f\u0131l\u0131mlar\u0131n \u015fekli<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poisson da\u011f\u0131l\u0131m\u0131 ile normal da\u011f\u0131l\u0131m aras\u0131ndaki ikinci fark da\u011f\u0131l\u0131mlar\u0131n \u015feklindedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Normal bir da\u011f\u0131l\u0131m<\/strong> her zaman \u00e7an \u015fekline sahip olacakt\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22710 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normepoisson1.jpg\" alt=\"\" width=\"416\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ancak Poisson da\u011f\u0131l\u0131m\u0131n\u0131n \u015fekli da\u011f\u0131l\u0131m\u0131n ortalama de\u011ferine ba\u011fl\u0131 olarak de\u011fi\u015fmektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, <strong>\u03bc = 3<\/strong> gibi ortalama de\u011feri k\u00fc\u00e7\u00fck olan bir Poisson da\u011f\u0131l\u0131m\u0131 g\u00fc\u00e7l\u00fc bir \u015fekilde <a href=\"https:\/\/statorials.org\/tr\/sol-onyargi-ve-sag-onyargi\/\" target=\"_blank\" rel=\"noopener\">sa\u011fa \u00e7arp\u0131k<\/a> olacakt\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22713 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normepoisson3.jpg\" alt=\"\" width=\"410\" height=\"386\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ancak <strong>\u03bc = 20<\/strong> gibi daha b\u00fcy\u00fck bir ortalama de\u011fere sahip bir Poisson da\u011f\u0131l\u0131m\u0131, t\u0131pk\u0131 normal da\u011f\u0131l\u0131m gibi \u00e7an \u015fekli sergileyecektir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22715 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normepoisson4-1.jpg\" alt=\"\" width=\"403\" height=\"390\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bir Poisson da\u011f\u0131l\u0131m\u0131n\u0131n alt s\u0131n\u0131r\u0131n\u0131n, ortalaman\u0131n de\u011ferinden ba\u011f\u0131ms\u0131z olarak her zaman s\u0131f\u0131r olaca\u011f\u0131n\u0131 unutmay\u0131n, \u00e7\u00fcnk\u00fc bir Poisson da\u011f\u0131l\u0131m\u0131 yaln\u0131zca s\u0131f\u0131ra e\u015fit veya s\u0131f\u0131rdan b\u00fcy\u00fck tam say\u0131 de\u011ferleri ile kullan\u0131labilir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler Poisson da\u011f\u0131l\u0131m\u0131 hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/balik-dagitimi\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131na giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/poisson-dagilimi-varsayimlari\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131n\u0131n d\u00f6rt hipotezi<\/a><br \/><a href=\"https:\/\/statorials.org\/tr\/balik-dagitimi-gercek-ornekleri\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131n\u0131n 5 somut \u00f6rne\u011fi<\/a><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler normal da\u011f\u0131l\u0131m hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> Normal da\u011f\u0131l\u0131ma giri\u015f<br \/> <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim-ornegi\/\" target=\"_blank\" rel=\"noopener\">Normal da\u011f\u0131l\u0131m\u0131n 6 somut \u00f6rne\u011fi<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim-veri-kumesi-olusturucu\/\" target=\"_blank\" rel=\"noopener\">Normal Da\u011f\u0131t\u0131m Veri K\u00fcmesi Olu\u015fturucu<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Poisson da\u011f\u0131l\u0131m\u0131 ve normal da\u011f\u0131l\u0131m istatistikte en s\u0131k kullan\u0131lan olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131ndan ikisidir. Bu e\u011fitimde her da\u011f\u0131t\u0131m\u0131n h\u0131zl\u0131 bir a\u00e7\u0131klamas\u0131n\u0131n yan\u0131 s\u0131ra da\u011f\u0131t\u0131mlar aras\u0131ndaki iki \u00f6nemli fark da sunulmaktad\u0131r. Genel bak\u0131\u015f: Poisson da\u011f\u0131l\u0131m\u0131 Poisson da\u011f\u0131l\u0131m\u0131 belirli bir zaman aral\u0131\u011f\u0131nda k ba\u015far\u0131 elde etme olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klar. Bir Xrastgele de\u011fi\u015fkeni bir Poisson da\u011f\u0131l\u0131m\u0131n\u0131 takip ediyorsa, X = k [&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-2556","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 da\u011f\u0131l\u0131m\u0131 ve normal da\u011f\u0131l\u0131m: fark nedir? - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde Poisson da\u011f\u0131l\u0131m\u0131 ile normal da\u011f\u0131l\u0131m aras\u0131ndaki farklar birka\u00e7 \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/balik-ve-normal-dagilim\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Poisson da\u011f\u0131l\u0131m\u0131 ve normal da\u011f\u0131l\u0131m: fark nedir? 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