\u0130lk rakam kanunu<\/strong> olarak da adland\u0131r\u0131lan Benford yasas\u0131<\/strong> , bir veri par\u00e7as\u0131n\u0131n ilk rakam\u0131n\u0131n 1 olma olas\u0131l\u0131\u011f\u0131n\u0131n ba\u015fka bir say\u0131 olma olas\u0131l\u0131\u011f\u0131ndan daha b\u00fcy\u00fck oldu\u011funu s\u00f6yleyen istatistiksel bir yasad\u0131r.<\/p>\n
Yani Benford kanunu, ger\u00e7ek hayatta var olan bir say\u0131sal veri k\u00fcmesinde 1 say\u0131s\u0131n\u0131n, verinin ilk basama\u011f\u0131 olarak en \u00e7ok tekrarlanan say\u0131 oldu\u011funu s\u00f6yl\u00fcyor.<\/p>\n
Ayr\u0131ca say\u0131 ne kadar y\u00fcksek olursa birinci olma ihtimali de o kadar d\u00fc\u015f\u00fck olur. Bu nedenle, ilk say\u0131n\u0131n 1 olma olas\u0131l\u0131\u011f\u0131 2’den daha y\u00fcksektir, ancak 2’nin olas\u0131l\u0131\u011f\u0131 3’ten daha y\u00fcksektir, 3’\u00fcn olas\u0131l\u0131\u011f\u0131 4’ten daha y\u00fcksektir vb.<\/p>\n
Benford yasas\u0131 ad\u0131n\u0131 Amerikal\u0131 Frank Benford’a bor\u00e7ludur. Benford bunu icat etmemi\u015f olmas\u0131na ra\u011fmen bu istatistiksel kural\u0131 pop\u00fcler hale getirdi. A\u015fa\u011f\u0131da Benford yasas\u0131n\u0131n k\u00f6kenini g\u00f6rece\u011fiz. <\/p>\n
Benford Yasas\u0131, ilk rakam\u0131n belirli bir say\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131n, o say\u0131n\u0131n bir art\u0131 bir b\u00f6l\u00fc logaritmas\u0131na e\u015fit oldu\u011funu belirtir.<\/p>\n
Benford yasas\u0131n\u0131n form\u00fcl\u00fc<\/strong> bu nedenle a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n
<\/p>\n<\/p>\n
Bu nedenle Benford yasas\u0131 form\u00fcl\u00fcnden her say\u0131n\u0131n bir veri \u00f6\u011fesinin ilk basama\u011f\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131 \u00e7\u0131karabiliriz. A\u015fa\u011f\u0131daki tabloda t\u00fcm olas\u0131l\u0131klar\u0131n y\u00fczdelerini g\u00f6rebilirsiniz: <\/p>\n
\n
\n\n
\n
Fig\u00fcr<\/th>\n
Olas\u0131l\u0131k ilk numara ol<\/th>\n<\/tr>\n<\/thead>\n
Ek olarak, a\u015fa\u011f\u0131da Benford yasas\u0131n\u0131n t\u00fcm olas\u0131l\u0131klar\u0131n\u0131n grafiksel olarak temsil edildi\u011fi bir histogram\u0131 g\u00f6rebilirsiniz: <\/p>\n<\/figure>\n
1881’de matematik\u00e7i Simon Newcomb, logaritma tablolar\u0131n\u0131n ilk sayfalar\u0131n\u0131n son sayfalar\u0131ndan \u00e7ok daha fazla kullan\u0131ld\u0131\u011f\u0131n\u0131 ke\u015ffetti\u011finde Benford yasas\u0131n\u0131 \u00e7\u0131kard\u0131. Bu, say\u0131lar\u0131n ilk rakamlar\u0131n\u0131n e\u015fit olas\u0131l\u0131kl\u0131 olmad\u0131\u011f\u0131, ancak 1’in 2’den daha s\u0131k oldu\u011fu, 2’nin 3’ten daha s\u0131k oldu\u011fu ve bu \u015fekilde 9’a kadar devam etti\u011fi anlam\u0131na geliyordu.<\/p>\n
Ancak Newcomb bu kural\u0131n takip edildi\u011fine dair hi\u00e7bir istatistiksel kan\u0131t b\u0131rakmad\u0131; yaln\u0131zca logaritmik tablolar\u0131n a\u015f\u0131nma ve y\u0131pranmas\u0131ndan bir \u00e7\u0131kar\u0131m yapt\u0131.<\/p>\n
Daha sonra, \u00f6zellikle 1938’de fizik\u00e7i Frank Benford ayn\u0131 g\u00f6zlemi yapt\u0131 ve bunu ampirik olarak do\u011frulamak i\u00e7in bir deney yapt\u0131. 20 farkl\u0131 \u00f6rnekten al\u0131nan 20.229 de\u011ferden olu\u015fan istatistiksel veri seti \u00fczerinde, her verinin ilk rakam\u0131 \u00fczerinde bir \u00e7al\u0131\u015fma ger\u00e7ekle\u015ftirdi. B\u00f6ylece sonu\u00e7lara dayanarak Benford yasas\u0131n\u0131n ger\u00e7ekle\u015fti\u011fini g\u00f6sterdi ve ilk rakam\u0131n belirli bir say\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamas\u0131na olanak tan\u0131yan form\u00fcl\u00fc \u00e7\u0131kard\u0131 (bu form\u00fcl\u00fc yukar\u0131da g\u00f6rd\u00fck).<\/p>\n
K\u0131sacas\u0131 Benford Yasas\u0131 ilk kez Simon Newcomb taraf\u0131ndan ke\u015ffedilmi\u015f olsa da bu istatistik yasas\u0131n\u0131 do\u011frulayan ki\u015fi oldu\u011fu i\u00e7in kendisine Frank Benford’un ad\u0131 verilmi\u015ftir. <\/p>\n
Benford yasas\u0131, \u00e7ok farkl\u0131 alanlarda uygulama alan\u0131 bulan istatistiksel bir yasad\u0131r. \u00d6rne\u011fin Benford yasas\u0131 ekonomide, biyolojide ve hatta politikada yayg\u0131n olarak kullan\u0131lmaktad\u0131r.<\/p>\n
Ekonomide, Benford yasas\u0131 genellikle veri manip\u00fclasyonunu tespit etmek i\u00e7in kullan\u0131l\u0131r, \u00e7\u00fcnk\u00fc bir veri seti Benford yasas\u0131na uymuyorsa, bu verinin manip\u00fcle edildi\u011fini g\u00f6sterir. Bu yasa, \u00f6rne\u011fin olas\u0131 vergi ka\u00e7ak\u00e7\u0131l\u0131\u011f\u0131 vakalar\u0131n\u0131 tespit etmek i\u00e7in kullan\u0131l\u0131yor.<\/p>\n
Sonu\u00e7lar e\u015fit olas\u0131l\u0131kl\u0131 oldu\u011fundan Benford yasas\u0131n\u0131n rastgele olaylar\u0131n do\u011frulu\u011funu g\u00f6stermek i\u00e7in kullan\u0131lmad\u0131\u011f\u0131na dikkat edilmelidir. Bu nedenle Benford kural\u0131 piyango sonu\u00e7lar\u0131n\u0131 do\u011frulamak i\u00e7in kullan\u0131lamaz.<\/p>\n
\u00d6te yandan genetikte Benford yasas\u0131, farkl\u0131 organizma t\u00fcrleri aras\u0131ndaki genom uzunlu\u011fundaki farkl\u0131l\u0131klar\u0131 analiz etmek i\u00e7in kullan\u0131labilir.<\/p>\n
Son olarak, Benford yasas\u0131n\u0131 uygulayarak se\u00e7men sahtekarl\u0131\u011f\u0131n\u0131 tespit etmek i\u00e7in de giri\u015fimlerde bulunuldu, ancak bu davadaki yararl\u0131l\u0131\u011f\u0131 sorguland\u0131.<\/p>\n","protected":false},"excerpt":{"rendered":"
Bu makale Benford yasas\u0131n\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Ayr\u0131ca Benford yasas\u0131n\u0131n nas\u0131l ke\u015ffedildi\u011fini ve bu istatistik yasas\u0131n\u0131n uygulamalar\u0131n\u0131n neler oldu\u011funu g\u00f6rebileceksiniz. Benford Yasas\u0131 Nedir? \u0130lk rakam kanunu olarak da adland\u0131r\u0131lan Benford yasas\u0131 , bir veri par\u00e7as\u0131n\u0131n ilk rakam\u0131n\u0131n 1 olma olas\u0131l\u0131\u011f\u0131n\u0131n ba\u015fka bir say\u0131 olma olas\u0131l\u0131\u011f\u0131ndan daha b\u00fcy\u00fck oldu\u011funu s\u00f6yleyen istatistiksel bir yasad\u0131r. Yani Benford kanunu, […]<\/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-230","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"\n
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![\"\\begin{array}{c}\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a77defb5b209293a074ac2bee02c2e07_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"Benford](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/loi-de-benford.png\")
<\/figure>\n