{"id":1564,"date":"2023-07-25T21:11:46","date_gmt":"2023-07-25T21:11:46","guid":{"rendered":"https:\/\/statorials.org\/tr\/shannon-cesitlilik-indeksi\/"},"modified":"2023-07-25T21:11:46","modified_gmt":"2023-07-25T21:11:46","slug":"shannon-cesitlilik-indeksi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/shannon-cesitlilik-indeksi\/","title":{"rendered":"Shannon \u00e7e\u015fitlilik endeksi: tan\u0131m ve \u00f6rnekler"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Shannon \u00e7e\u015fitlilik endeksi<\/strong> (bazen Shannon-Wiener endeksi olarak da adland\u0131r\u0131l\u0131r), bir topluluk i\u00e7indeki t\u00fcrlerin \u00e7e\u015fitlili\u011fini \u00f6l\u00e7menin bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Not <em>H<\/em> , bu endeks a\u015fa\u011f\u0131daki gibi hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>H<\/em> = -\u03a3 <em>p<\/em> <sub>ben<\/sub> * <em>ln(p<\/em> <sub>ben<\/sub> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3:<\/strong> \u201ctoplam\u201d anlam\u0131na gelen Yunanca bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>ln<\/em> :<\/strong> Do\u011fal g\u00fcnl\u00fck<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>pi<\/em> <sub>i<\/sub> :<\/strong> <em>i<\/em> t\u00fcrlerinden olu\u015fan t\u00fcm toplulu\u011fun oran\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><em>H<\/em> de\u011feri ne kadar y\u00fcksek olursa, belirli bir topluluktaki t\u00fcr \u00e7e\u015fitlili\u011fi de o kadar y\u00fcksek olur. <em>H<\/em> de\u011feri ne kadar d\u00fc\u015f\u00fck olursa \u00e7e\u015fitlilik de o kadar d\u00fc\u015f\u00fck olur. <em>H<\/em> de\u011feri = 0, yaln\u0131zca bir t\u00fcr\u00fcn bulundu\u011fu bir toplulu\u011fu belirtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Shannon&#8217;\u0131n e\u015fitlik endeksi, bir topluluktaki t\u00fcrlerin e\u015fitli\u011fini \u00f6l\u00e7menin bir yoludur. &#8220;Tekd\u00fczelik&#8221; terimi basit\u00e7e topluluk i\u00e7indeki farkl\u0131 t\u00fcrlerin bollu\u011fundaki benzerli\u011fi ifade eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Not: <em><sub>EH<\/sub><\/em> , bu endeks \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>E <sub>H<\/sub><\/em> = <em>H<\/em> \/ <em>ln<\/em> ( <em>S<\/em> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><em>H<\/em> :<\/strong> Shannon&#8217;\u0131n \u00e7e\u015fitlilik indeksi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>S<\/em> :<\/strong> Benzersiz t\u00fcrlerin toplam say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu de\u011fer 0 ila 1 aras\u0131nda de\u011fi\u015fir; burada 1, tam e\u015fitli\u011fi belirtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ad\u0131m ad\u0131m \u00f6rnek, belirli bir topluluk i\u00e7in Shannon \u00c7e\u015fitlilik Endeksi&#8217;nin ve Shannon Hisse Senedi Endeksi&#8217;nin nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>1. Ad\u0131m: Verileri toplay\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir biyolo\u011fun yerel bir ormandaki t\u00fcr \u00e7e\u015fitlili\u011fini \u00f6l\u00e7mek istedi\u011fini varsayal\u0131m. A\u015fa\u011f\u0131daki verileri toplar:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15477 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon1.png\" alt=\"\" width=\"158\" height=\"186\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Oranlar\u0131 hesaplay\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra biyolog her t\u00fcrden olu\u015fan toplulu\u011fun oran\u0131n\u0131 hesaplayabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, toplam 105 birey var ve 40&#8217;\u0131 A t\u00fcr\u00fc olarak s\u0131n\u0131fland\u0131r\u0131l\u0131yor. Dolay\u0131s\u0131yla A t\u00fcr\u00fc, toplam toplulu\u011fun 40\/105 = <strong>0,38&#8217;ini<\/strong> temsil ediyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her t\u00fcr i\u00e7in benzer bir hesaplama yapabilir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-15478 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon2.png\" alt=\"\" width=\"251\" height=\"194\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Oranlar\u0131n do\u011fal logaritmas\u0131n\u0131 hesaplay\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra her oran\u0131n do\u011fal logaritmas\u0131n\u0131 hesaplayabilir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15479 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon3.png\" alt=\"\" width=\"299\" height=\"179\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: Oranlar\u0131 oranlar\u0131n do\u011fal logaritmas\u0131 ile \u00e7arp\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha sonra oranlar\u0131 oranlar\u0131n do\u011fal logaritmas\u0131yla \u00e7arpabilir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15480 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon4.png\" alt=\"\" width=\"376\" height=\"181\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ad\u0131m 5: Shannon \u00c7e\u015fitlilik Endeksi&#8217;ni hesaplay\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Son olarak Shannon \u00e7e\u015fitlilik indeksini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>H<\/em> = -\u03a3 <em>p<\/em> <sub>ben<\/sub> * <em>ln(p<\/em> <sub>ben<\/sub> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte, son s\u00fctundaki toplam\u0131 al\u0131p negatif olanla \u00e7arpabilir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-15481 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon5.png\" alt=\"Shannon \u00c7e\u015fitlilik Endeksi \u00d6rne\u011fi\" width=\"397\" height=\"220\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu toplulu\u011fun Shannon \u00c7e\u015fitlilik Endeksi <strong>1,49&#8217;dur<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Shannon Hisse Senedi Endeksi&#8217;ni hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc de kullanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>E <sub>H<\/sub><\/em> = <em>H<\/em> \/ <em>ln<\/em> ( <em>S<\/em> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte toplamda <em>S<\/em> =5 t\u00fcr var, dolay\u0131s\u0131yla bu indeksi \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><sub>EH<\/sub><\/em> = 1,49 \/ <em>ln<\/em> (5) = <strong>0,92<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Herhangi bir veri k\u00fcmesi i\u00e7in Shannon \u00c7e\u015fitlilik Endeksi&#8217;ni otomatik olarak hesaplamak amac\u0131yla bu Shannon \u00c7e\u015fitlilik Endeksi hesaplay\u0131c\u0131s\u0131n\u0131 kullanmaktan \u00e7ekinmeyin.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Shannon \u00e7e\u015fitlilik endeksi (bazen Shannon-Wiener endeksi olarak da adland\u0131r\u0131l\u0131r), bir topluluk i\u00e7indeki t\u00fcrlerin \u00e7e\u015fitlili\u011fini \u00f6l\u00e7menin bir yoludur. Not H , bu endeks a\u015fa\u011f\u0131daki gibi hesaplan\u0131r: H = -\u03a3 p ben * ln(p ben ) Alt\u0131n: \u03a3: \u201ctoplam\u201d anlam\u0131na gelen Yunanca bir sembol ln : Do\u011fal g\u00fcnl\u00fck pi i : i t\u00fcrlerinden olu\u015fan t\u00fcm toplulu\u011fun oran\u0131 [&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-1564","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>Shannon \u00e7e\u015fitlilik indeksi: tan\u0131m ve \u00f6rnek \u2013 Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, resmi bir tan\u0131m ve ad\u0131m ad\u0131m \u00f6rnek dahil olmak \u00fczere Shannon \u00c7e\u015fitlilik 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