{"id":1347,"date":"2023-07-26T19:00:35","date_gmt":"2023-07-26T19:00:35","guid":{"rendered":"https:\/\/statorials.org\/tr\/rayleigh-dagilimi\/"},"modified":"2023-07-26T19:00:35","modified_gmt":"2023-07-26T19:00:35","slug":"rayleigh-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rayleigh-dagilimi\/","title":{"rendered":"Rayleigh da\u011f\u0131l\u0131m\u0131na giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Rayleigh da\u011f\u0131l\u0131m\u0131,<\/strong> yaln\u0131zca s\u0131f\u0131ra e\u015fit veya s\u0131f\u0131rdan b\u00fcy\u00fck de\u011ferler alabilen <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noopener\">rastgele de\u011fi\u015fkenleri<\/a> modellemek i\u00e7in kullan\u0131lan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki olas\u0131l\u0131k yo\u011funluk fonksiyonuna sahiptir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">f(x; \u03c3) = (x\/\u03c3 <sup>2<\/sup> )e <sup>-x <sup>2<\/sup> \/(2\u03c3 <sup>2<\/sup> )<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">burada \u03c3 da\u011f\u0131l\u0131m\u0131n \u00f6l\u00e7ek parametresidir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Rayleigh da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Rayleigh da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Ortalama:<\/strong> \u03c3\u221a <span style=\"border-top: 1px solid black;\">\u03c0\/2<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Sapma:<\/strong> ((4-\u03c0)\/2)\u03c3 <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Mod:<\/strong> \u03c3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u03c0&#8217;nin bilinen bir say\u0131sal de\u011feri oldu\u011fundan, \u00f6zellikleri a\u015fa\u011f\u0131daki gibi basitle\u015ftirebiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Ortalama:<\/strong> 1.253\u03c3<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Sapma:<\/strong> 0,429\u03c3 <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Mod:<\/strong> \u03c3<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Rayleigh da\u011f\u0131l\u0131m\u0131n\u0131n g\u00f6rselle\u015ftirilmesi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki grafik, \u00f6l\u00e7ek parametresi i\u00e7in farkl\u0131 de\u011ferler ald\u0131\u011f\u0131ndan Rayleigh da\u011f\u0131l\u0131m\u0131n\u0131n \u015feklini g\u00f6stermektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13154 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/rayleigh1.png\" alt=\"Rayleigh olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131\" width=\"419\" height=\"377\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u00d6l\u00e7ek parametresi \u03c3&#8217;nun de\u011feri ne kadar b\u00fcy\u00fck olursa, da\u011f\u0131l\u0131m\u0131n da o kadar geni\u015f olaca\u011f\u0131na dikkat edin.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>Bonus:<\/strong> Merak edenler i\u00e7in yukar\u0131daki grafi\u011fi olu\u015fturmak i\u00e7in a\u015fa\u011f\u0131daki R kodunu kulland\u0131k:<\/span><\/em><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load VGAM package\n<\/span><span style=\"color: #008000;\">library<\/span> (VGAM)\n\n<span style=\"color: #008080;\">#create density plots\n<\/span>curve(drayleigh(x, scale = 0.5), from=0, to=10, col='green')\ncurve(drayleigh(x, scale = 1), from=0, to=10, col='red', add=TRUE)\ncurve(drayleigh(x, scale = 2), from=0, to=10, col='blue', add=TRUE)\ncurve(drayleigh(x, scale = 4), from=0, to=10, col='purple', add=TRUE)\n\n<span style=\"color: #008080;\">#add legend\n<\/span>legend(6, 1, legend=c(\"\u03c3=0.5\", \"\u03c3=1\", \"\u03c3=2\", \"\u03c3=4\"),\n       col=c(\"green\", \"red\", \"blue\", \"purple\"), lty=1, cex=1.2)\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Di\u011fer da\u011f\u0131t\u0131mlarla ili\u015fki<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Rayleigh da\u011f\u0131l\u0131m\u0131n\u0131n di\u011fer olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131yla a\u015fa\u011f\u0131daki ili\u015fkisi vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> \u00d6l\u00e7ek parametresi (\u03c3) <span style=\"color: #000000;\">1&#8217;e e\u015fit oldu\u011funda Rayleigh da\u011f\u0131l\u0131m\u0131 2 serbestlik derecesine sahip Ki-kare da\u011f\u0131l\u0131m\u0131na e\u015fittir.<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> Rayleigh da\u011f\u0131l\u0131m\u0131, \u015fekil parametresi k = 2 olan Weibull da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zel bir durumudur.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> \u00d6l\u00e7ek parametresi \u03c3 olan Rayleigh da\u011f\u0131l\u0131m\u0131, Rice(0, \u03c3) olan Rice da\u011f\u0131l\u0131m\u0131na e\u015fittir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Uygulamalar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Uygulamada Rayleigh da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131dakiler dahil \u00e7e\u015fitli uygulamalarda kullan\u0131l\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Rayleigh da\u011f\u0131l\u0131m\u0131, dalgalar\u0131n tepe noktas\u0131na ula\u015fmas\u0131 i\u00e7in ge\u00e7en s\u00fcre ve dalgalar\u0131n ula\u015ft\u0131\u011f\u0131 maksimum y\u00fckseklik dahil olmak \u00fczere, okyanustaki dalgalar\u0131n davran\u0131\u015f\u0131n\u0131 modellemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> Rayleigh da\u011f\u0131l\u0131m\u0131, daha yayg\u0131n olarak MRI olarak bilinen manyetik rezonans g\u00f6r\u00fcnt\u00fclemede arka plan verilerinin davran\u0131\u015f\u0131n\u0131 modellemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> Rayleigh da\u011f\u0131l\u0131m\u0131 beslenme alan\u0131nda, insanlarda ve hayvanlarda besin d\u00fczeyleri ile beslenme tepkisi aras\u0131ndaki ili\u015fkiyi modellemek i\u00e7in kullan\u0131l\u0131r.<\/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 istatistiklerdeki di\u011fer da\u011f\u0131l\u0131mlar hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> Normal da\u011f\u0131l\u0131ma giri\u015f<br \/> <a href=\"https:\/\/statorials.org\/tr\/binom-dagilimi-1\/\" target=\"_blank\" rel=\"noopener\">Binom da\u011f\u0131l\u0131m\u0131na giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/balik-dagitimi\/\" target=\"_blank\" rel=\"noopener\">Poisson da\u011f\u0131l\u0131m\u0131na giri\u015f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rayleigh da\u011f\u0131l\u0131m\u0131, yaln\u0131zca s\u0131f\u0131ra e\u015fit veya s\u0131f\u0131rdan b\u00fcy\u00fck de\u011ferler alabilen rastgele de\u011fi\u015fkenleri modellemek i\u00e7in kullan\u0131lan s\u00fcrekli bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131d\u0131r. A\u015fa\u011f\u0131daki olas\u0131l\u0131k yo\u011funluk fonksiyonuna sahiptir: f(x; \u03c3) = (x\/\u03c3 2 )e -x 2 \/(2\u03c3 2 ) burada \u03c3 da\u011f\u0131l\u0131m\u0131n \u00f6l\u00e7ek parametresidir. Rayleigh da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri Rayleigh da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir: Ortalama: \u03c3\u221a \u03c0\/2 Sapma: ((4-\u03c0)\/2)\u03c3 2 Mod: [&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-1347","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>Rayleigh Da\u011f\u0131t\u0131m\u0131na Giri\u015f - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitim, resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek de dahil olmak \u00fczere Rayleigh da\u011f\u0131l\u0131m\u0131na h\u0131zl\u0131 bir giri\u015f sa\u011flar.\" \/>\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\/rayleigh-dagilimi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rayleigh Da\u011f\u0131t\u0131m\u0131na Giri\u015f - 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