{"id":229,"date":"2023-08-03T22:21:12","date_gmt":"2023-08-03T22:21:12","guid":{"rendered":"https:\/\/statorials.org\/tr\/gunluk-normal-dagilim\/"},"modified":"2023-08-03T22:21:12","modified_gmt":"2023-08-03T22:21:12","slug":"gunluk-normal-dagilim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/gunluk-normal-dagilim\/","title":{"rendered":"Lognormal da\u011f\u0131l\u0131m"},"content":{"rendered":"<p>Bu makalede istatistikte lognormal da\u011f\u0131l\u0131m\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece lognormal da\u011f\u0131l\u0131m\u0131n \u00f6zelliklerinin neler oldu\u011funu ve bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011fini \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-lognormal\"><\/span> Lognormal da\u011f\u0131l\u0131m nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Lognormal da\u011f\u0131l\u0131m<\/strong> veya <strong>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<p> Bu nedenle, e\u011fer X de\u011fi\u015fkeni normal da\u011f\u0131l\u0131ma sahipse, \u00fcstel fonksiyon e <sup>x<\/sup> lognormal da\u011f\u0131l\u0131ma sahiptir.<\/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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Logaritman\u0131n yaln\u0131zca bir pozitif arg\u00fcman alan bir fonksiyon olmas\u0131 nedeniyle lognormal da\u011f\u0131l\u0131m\u0131n yaln\u0131zca de\u011fi\u015fken de\u011ferleri pozitif oldu\u011funda kullan\u0131labilece\u011fini unutmay\u0131n.<\/p>\n<p> 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<p> Lognormal da\u011f\u0131l\u0131m ayn\u0131 zamanda <strong>Tinaut da\u011f\u0131l\u0131m\u0131 olarak<\/strong> da bilinir ve bazen <strong>lognormal da\u011f\u0131l\u0131m<\/strong> veya <strong>log-normal da\u011f\u0131l\u0131m<\/strong> olarak da yaz\u0131l\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-lognormal\"><\/span> Lognormal da\u011f\u0131l\u0131m grafi\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k lognormal da\u011f\u0131l\u0131m\u0131n tan\u0131m\u0131n\u0131 bildi\u011fimize g\u00f6re, bu b\u00f6l\u00fcmde lognormal da\u011f\u0131l\u0131m\u0131n grafiksel g\u00f6steriminin, aritmetik ortalamas\u0131na ve standart sapmas\u0131na ba\u011fl\u0131 olarak nas\u0131l de\u011fi\u015fti\u011fini g\u00f6rece\u011fiz.<\/p>\n<p> Lognormal da\u011f\u0131l\u0131m\u0131n yo\u011funluk fonksiyonunun grafi\u011fi a\u015fa\u011f\u0131daki gibidir: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/trace-de-distribution-lognormale.png\" alt=\"lognormal da\u011f\u0131l\u0131m grafi\u011fi\" class=\"wp-image-4563\" width=\"675\" height=\"406\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6te yandan lognormal da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k grafi\u011fi \u015fu \u015fekildedir: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-de-probabilite-lognormale-cumulative.png\" alt=\"lognormal da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k grafi\u011fi\" class=\"wp-image-4564\" width=\"675\" height=\"404\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-lognormal\"><\/span> Lognormal da\u011f\u0131l\u0131m\u0131n \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Lognormal da\u011f\u0131l\u0131m a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li> Lognormal da\u011f\u0131l\u0131m iki parametrenin de\u011feriyle tan\u0131mlan\u0131r: aritmetik ortalamas\u0131 \u03bc ve varyans\u0131 \u03c3 <sup>2<\/sup> .<\/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-216d8f120f09a37cd8f797bb3b115a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{Lognormal}(\\mu,\\sigma^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Logaritman\u0131n negatif veya s\u0131f\u0131r de\u011ferleri kabul etmemesi nedeniyle lognormal da\u011f\u0131l\u0131m\u0131n alan\u0131 pozitif 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-f543506f97e1f9c5a56ccc4566a3febf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Lognormal da\u011f\u0131l\u0131m beklentisi, e say\u0131s\u0131n\u0131n ortalaman\u0131n toplam\u0131 art\u0131 varyans\u0131n ikiye b\u00f6l\u00fcnmesine 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-109a1024d530b2993db41f1d7a5a24c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E[X]=e^{\\mu+\\frac{\\sigma^2}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u00d6te yandan lognormal da\u011f\u0131l\u0131m\u0131n varyans\u0131 a\u015fa\u011f\u0131daki ifadeyle hesaplanabilir:<\/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-5afc17462bb71082888ab755626b853a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\left(e^{\\sigma^2}-1\\right)\\cdot e^{2\\mu+\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"223\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li> Lognormal da\u011f\u0131l\u0131m\u0131n modu, da\u011f\u0131l\u0131m\u0131n ortalamas\u0131na y\u00fckseltilen e say\u0131s\u0131na 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-21b2bd4c45dca8e305c9ee480d961f4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=e^\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Lognormal da\u011f\u0131l\u0131m\u0131n \u00e7arp\u0131kl\u0131k katsay\u0131s\u0131 a\u015fa\u011f\u0131daki form\u00fcl uygulanarak 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-2686fd41c4e28d5c396bf494229a63a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\left(e^{\\sigma^2}+2\\right)\\cdot\\sqrt{e^{\\sigma^2}-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"198\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<ul>\n<li> Lognormal da\u011f\u0131l\u0131m\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-25698732745689402d16ea353a072cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{1}{\\sigma \\cdot x\\cdot \\sqrt{2 \\pi}}\\cdot \\exp\\left(-\\frac{(\\ln x-\\mu)^2}{2\\sigma^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"347\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Lognormal da\u011f\u0131l\u0131m\u0131n k\u00fcm\u00fclatif olas\u0131l\u0131k 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-59c2474703bad4805a6a44bd05cf92bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\Phi\\left(\\frac{\\ln x-\\mu}{\\sigma}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"200\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/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-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Phi\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/normal-standart-dagilim\/\">standart normal da\u011f\u0131l\u0131m\u0131n<\/a> k\u00fcm\u00fclatif olas\u0131l\u0131k fonksiyonudur.<\/p>\n<ul>\n<li> Lognormal da\u011f\u0131l\u0131m\u0131n aritmetik ortalamas\u0131, medyan\u0131n de\u011ferinden daha b\u00fcy\u00fckt\u00fcr.<\/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-96e66e8c60e4ce5e235c30258e4ecead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu > Me&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;16&#8243; width=&#8221;61&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede istatistikte lognormal da\u011f\u0131l\u0131m\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece lognormal da\u011f\u0131l\u0131m\u0131n \u00f6zelliklerinin neler oldu\u011funu ve bu t\u00fcr olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n grafi\u011fini \u00f6\u011freneceksiniz. Lognormal da\u011f\u0131l\u0131m nedir? Lognormal da\u011f\u0131l\u0131m veya lognormal da\u011f\u0131l\u0131m , 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. Bu nedenle, e\u011fer X de\u011fi\u015fkeni normal da\u011f\u0131l\u0131ma sahipse, \u00fcstel fonksiyon e x lognormal da\u011f\u0131l\u0131ma [&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-229","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 Lognormal da\u011f\u0131l\u0131m<\/title>\n<meta name=\"description\" content=\"Burada lognormal da\u011f\u0131l\u0131m\u0131n ne oldu\u011funu, lognormal da\u011f\u0131l\u0131m\u0131n \u00f6zelliklerinin neler oldu\u011funu ve grafiksel g\u00f6sterimini \u00f6\u011freneceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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