{"id":231,"date":"2023-08-03T21:54:17","date_gmt":"2023-08-03T21:54:17","guid":{"rendered":"https:\/\/statorials.org\/tr\/pareto-kanunu\/"},"modified":"2023-08-03T21:54:17","modified_gmt":"2023-08-03T21:54:17","slug":"pareto-kanunu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/pareto-kanunu\/","title":{"rendered":"Pareto da\u011f\u0131l\u0131m\u0131"},"content":{"rendered":"<p>Bu makalede istatistikte Pareto da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayr\u0131ca Pareto da\u011f\u0131l\u0131m grafi\u011fini ve bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerini de g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-de-pareto\"><\/span> Pareto da\u011f\u0131l\u0131m\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>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<p> 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<p> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n iki karakteristik parametresi vard\u0131r: \u00f6l\u00e7ek parametresi x <sub>m<\/sub> ve \u015fekil parametresi \u03b1.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 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 servet 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<p> Pareto da\u011f\u0131l\u0131m\u0131, ad\u0131n\u0131 da\u011f\u0131l\u0131m\u0131 form\u00fcle eden ekonomist Vilfredo Pareto&#8217;dan alm\u0131\u015ft\u0131r. Ancak en \u00e7ok Pareto \u015femas\u0131yla tan\u0131n\u0131r. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/pareto-grafigi\/\">Pareto \u015femas\u0131 nedir?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-de-pareto\"><\/span> Pareto da\u011f\u0131l\u0131m tablosu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k Pareto da\u011f\u0131l\u0131m\u0131n\u0131n tan\u0131m\u0131n\u0131 bildi\u011fimize g\u00f6re, grafiksel olarak temsil edilen \u00e7e\u015fitli Pareto da\u011f\u0131l\u0131m \u00f6rneklerine bakal\u0131m.<\/p>\n<p> A\u015fa\u011f\u0131da Pareto da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonunun grafi\u011finin karakteristik de\u011ferlerine ba\u011fl\u0131 olarak nas\u0131l g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc g\u00f6rebilirsiniz: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-de-pareto.png\" alt=\"Pareto Da\u011f\u0131l\u0131m Tablosu\" class=\"wp-image-4774\" width=\"587\" height=\"413\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n etki alan\u0131n\u0131n x <sub>m<\/sub> de\u011ferinden +\u221e&#8217;a gitti\u011fine dikkat edin, bu nedenle yo\u011funluk fonksiyonu x <sub>m<\/sub> de\u011ferinden \u00f6nce mevcut de\u011fildir.<\/p>\n<p> \u00d6te yandan Pareto da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonunun grafi\u011fi \u015fu \u015fekildedir: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-de-probabilite-pareto-cumulative.png\" alt=\"Pareto da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131\" class=\"wp-image-4775\" width=\"589\" height=\"414\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-de-pareto\"><\/span> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k teorisi ve istatistik ile ilgili Pareto da\u011f\u0131l\u0131m\u0131n\u0131n en \u00f6nemli \u00f6zellikleri a\u015fa\u011f\u0131da verilmi\u015ftir.<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n e\u011frisini tan\u0131mlayan iki karakteristik parametresi vard\u0131r: \u00f6l\u00e7ek parametresi x <sub>m<\/sub> ve \u015fekil parametresi \u03b1.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c13a66a388e0a7e26781a0e8d9645f40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Pareto}(\\alpha,x_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n alan\u0131, \u00f6l\u00e7ek parametresinden art\u0131 sonsuza kadar t\u00fcm ger\u00e7ek say\u0131lardan olu\u015fur.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c720ee182b49a794ed2862dd83a10ca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in [x_m,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> E\u011fer \u03b1 1&#8217;den b\u00fcy\u00fckse, Pareto da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 \u03b1 \u00e7arp\u0131 x <sub>m<\/sub> ve \u03b1 eksi 1&#8217;in \u00e7arp\u0131m\u0131na e\u015fittir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6d26513868f9ed6fa45ab0fde0030884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=\\cfrac{\\alpha\\cdot x_m}{\\alpha-1}\\quad\\text{para } \\alpha>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;34&#8243; width=&#8221;214&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131, da\u011f\u0131l\u0131m\u0131n iki karakteristik parametresine ba\u011fl\u0131d\u0131r ve a\u015fa\u011f\u0131daki form\u00fclle hesaplan\u0131r:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6120976b3586b76661d13bb9fdd5375d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Var(X)=\\frac{x_\\mathrm{m}^2\\cdot \\alpha}{(\\alpha-1)^2\\cdot(\\alpha-2)}\\quad \\text{para }\\alpha>2&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;323&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n medyan\u0131 a\u015fa\u011f\u0131daki ifadeyle belirlenebilir:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0dc2c772a0a0662ad05f8b22c3cf1ba1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Me=x_\\mathrm{m}\\cdot \\sqrt[\\alpha]{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"113\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n modu, da\u011f\u0131l\u0131m\u0131n x <sub>m<\/sub> \u00f6l\u00e7ek parametresine e\u015fde\u011ferdir.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-494f2f6e64851f90c504c989d93e22dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n yo\u011funluk fonksiyonunun form\u00fcl\u00fc \u015f\u00f6yledir:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1e182771cfe3bf9a145a2ee59b9c7eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\alpha\\cdot x_m^\\alpha}{x^{\\alpha+1}}\\quad\\text{para }x\\geq x_m\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"262\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Benzer \u015fekilde Pareto da\u011f\u0131l\u0131m\u0131n\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonu form\u00fcl\u00fc \u015f\u00f6yledir:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-480adc7841b7c72cb4bfecb446ed3fab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=1-\\left(\\frac{x_\\mathrm{m}}{x}\\right)^\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"184\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n asimetri katsay\u0131s\u0131 yaln\u0131zca \u015fekil parametresi \u03b1&#8217;ya ba\u011fl\u0131d\u0131r ve ifadesi \u015f\u00f6yledir:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-98e7ba5f5d32988033c0f33d6af1bef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{2(1+\\alpha)}{\\alpha-3}\\,\\sqrt{\\frac{\\alpha-2}{\\alpha}}\\quad\\text{para }\\alpha>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;43&#8243; width=&#8221;274&#8243; style=&#8221;vertical-align: -14px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Pareto da\u011f\u0131l\u0131m\u0131n\u0131n bas\u0131kl\u0131k katsay\u0131s\u0131 da \u03b1 parametresinin de\u011ferine ba\u011fl\u0131 olarak de\u011fi\u015fir ve a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\u0131r:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-989019815fbeb266226cff9aa6b4a52b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{6(\\alpha^3+\\alpha^2-6\\alpha-2)}{\\alpha(\\alpha-3)(\\alpha-4)}\\quad\\text{para }\\alpha>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;44&#8243; width=&#8221;299&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede istatistikte Pareto da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayr\u0131ca Pareto da\u011f\u0131l\u0131m grafi\u011fini ve bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerini de g\u00f6rebileceksiniz. Pareto da\u011f\u0131l\u0131m\u0131 nedir? Pareto da\u011f\u0131l\u0131m\u0131, 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 [&hellip;]<\/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-231","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Pareto da\u011f\u0131l\u0131m\u0131<\/title>\n<meta name=\"description\" content=\"Burada Pareto da\u011f\u0131l\u0131m\u0131n\u0131n ne oldu\u011funu, ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131, grafi\u011fini ve Pareto da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zelliklerinin neler oldu\u011funu 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