{"id":4063,"date":"2026-10-15T02:24:01","date_gmt":"2026-10-15T01:24:01","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/istatistik\/shannon-entropi-hesaplayici\/"},"modified":"2026-10-15T02:24:01","modified_gmt":"2026-10-15T01:24:01","slug":"shannon-entropi-hesaplayici","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/shannon-entropi-hesaplayici\/","title":{"rendered":"Shannon Entropi Hesaplay\u0131c\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Bir Da\u011f\u0131l\u0131m\u0131n Belirsizli\u011fini \u00d6l\u00e7\u00fcn<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4063\" data-favorite-title=\"Shannon Entropisi\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/shannon-entropi-hesaplayici\/\" data-favorite-excerpt=\"Herhangi bir olas\u0131l\u0131k ya da say\u0131m k\u00fcmesinin Shannon entropisini hesaplay\u0131n. Kategori ba\u015f\u0131na de\u011ferleri girin, bir logaritma taban\u0131 se\u00e7in (bit, nat veya dit) ve H de\u011ferini, maksimum entropiyi ve verimlilik oran\u0131n\u0131 al\u0131n.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-wpcalc-dice\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/istatistik\/shannon-entropi-hesaplayici\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4063\" data-post=\"4063\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Kategori olas\u0131l\u0131klar\u0131 veya frekanslar<\/label><textarea id=\"field-1\" name=\"kategori_olaslklar_veya_frekanslar\">40; 30; 20; 10<\/textarea><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Girdi t\u00fcr\u00fc<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"girdi_tr\"><option value=\"auto\" selected>Otomatik alg\u0131la<\/option><option value=\"probs\">Olas\u0131l\u0131klar (toplam\u0131 1 olmal\u0131)<\/option><option value=\"counts\">Frekanslar (normalize edilir)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Logaritma taban\u0131<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"logaritma_taban\"><option value=\"2\" selected>2 \u2014 bit<\/option><option value=\"10\">10 \u2014 dit (hartley)<\/option><option value=\"e\">e \u2248 2,718 \u2014 nat<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4063\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Shannon Entropisi Sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Shannon entropisi<\/span><span class=\"result-term\">H<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Olas\u0131 en y\u00fcksek entropi (k kategori \u00fczerinde d\u00fczg\u00fcn da\u011f\u0131l\u0131m)<\/span><span class=\"result-term\">H_max<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Entropinin maksimuma oran\u0131 (etkinlik)<\/span><span class=\"result-term\">H \/ H_max<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Kategori baz\u0131nda katk\u0131<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>Bu entropi nas\u0131l hesapland\u0131<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4063\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Shannon Entropisi Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ H = -\\sum_{i=1}^{k} p_i \\log_b p_i = \\sum_{i=1}^{k} p_i \\log_b \\frac{1}{p_i} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Form\u00fcldeki simgeler:<\/strong><\/p>\n<ul>\n<li>\\(p_i\\) \u2014 \\(i\\). kategorinin olas\u0131l\u0131\u011f\u0131 (say\u0131mlar normalize edilir: \\(p_i = n_i \/ n\\))<\/li>\n<li>\\(k\\) \u2014 kategori say\u0131s\u0131<\/li>\n<li>\\(b\\) \u2014 logaritma taban\u0131: 2 bit, \\(e\\) nat, 10 dit (hartley) verir<\/li>\n<\/ul>\n<p>Form\u00fcl, da\u011f\u0131l\u0131mdan \u00e7ekilen bir sonucun ortalama s\u00fcrprizini, yani bilgi i\u00e7eri\u011fini ifade eder: her terim, bir kategorinin \\(\\log_b(1\/p_i)\\) bilgisini, o kategorinin ger\u00e7ekle\u015fme s\u0131kl\u0131\u011f\u0131yla a\u011f\u0131rl\u0131kland\u0131r\u0131r.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Shannon Entropisi \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> 100 ki\u015filik bir ankette kat\u0131l\u0131mc\u0131lara d\u00f6rt markadan favorileri sorulmu\u015f ve say\u0131mlar 40, 30, 20 ile 10 olarak bulunmu\u015f. Say\u0131mlar \\(p = (0.4,\\ 0.3,\\ 0.2,\\ 0.1)\\) olas\u0131l\u0131klar\u0131na normalize edilir ve taban 2'dir (bit).<\/p>\n<p>\\[ H = -(0.4\\log_2 0.4 + 0.3\\log_2 0.3 + 0.2\\log_2 0.2 + 0.1\\log_2 0.1) \\]<\/p>\n<p>\\[ H = 0.5288 + 0.5211 + 0.4644 + 0.3322 = 1.8464 \\text{ bit} \\]<\/p>\n<p>\\[ H_{max} = \\log_2 4 = 2 \\text{ bit}, \\quad \\frac{H}{H_{max}} = \\frac{1.8464}{2} = 0.9232 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(H \\approx 1.8464\\) bit, yani maksimumun %92,32'si \u2014 d\u00f6rt kategorisine neredeyse e\u015fit yay\u0131lm\u0131\u015f bir da\u011f\u0131l\u0131m.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>De\u011ferlerinizi <strong>Kategori olas\u0131l\u0131klar\u0131 veya say\u0131mlar\u0131<\/strong> alan\u0131na girin \u2014 kategori ba\u015f\u0131na bir de\u011fer; bo\u015fluk, noktal\u0131 virg\u00fcl ya da sat\u0131r sonuyla ay\u0131r\u0131n. Olas\u0131l\u0131k (\u00f6rn. 0,5; 0,25; 0,25) veya ham say\u0131m (\u00f6rn. 40; 30; 20; 10) yazabilirsiniz; ondal\u0131kl\u0131 virg\u00fcl de kabul edilir.<\/li>\n<li><strong>Giri\u015f t\u00fcr\u00fcn\u00fc<\/strong> \"Otomatik alg\u0131la\" olarak b\u0131rak\u0131n (toplam\u0131 1 olan de\u011ferler olas\u0131l\u0131k kabul edilir) ya da otomatik se\u00e7im belirsiz kal\u0131yorsa \"Olas\u0131l\u0131klar (toplam\u0131 1 olmal\u0131)\" veya \"Say\u0131m \/ frekans (normalize edilir)\" se\u00e7ene\u011fini elle belirleyin.<\/li>\n<li><strong>Logaritma taban\u0131n\u0131<\/strong> se\u00e7in: bit i\u00e7in 2, nat i\u00e7in \\(e\\), dit (hartley) i\u00e7in 10.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: <strong>Shannon entropisi<\/strong> H, kategori say\u0131n\u0131za g\u00f6re <strong>m\u00fcmk\u00fcn olan en y\u00fcksek entropi<\/strong> \\(H_{max}\\), <strong>verimlilik<\/strong> oran\u0131 \\(H\/H_{max}\\) ve her olas\u0131l\u0131\u011f\u0131, bilgi i\u00e7eri\u011fini ile H'ye katk\u0131s\u0131n\u0131 g\u00f6steren kategori bazl\u0131 d\u00f6k\u00fcm.<\/li>\n<\/ol>\n<h2>Shannon Entropisi Nedir?<\/h2>\n<p>Claude Shannon'\u0131n 1948'de ortaya koydu\u011fu Shannon entropisi, bir olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n belirsizli\u011fini \u00f6l\u00e7er: ortalama olarak hangi kategorinin ger\u00e7ekle\u015fece\u011fini \u00f6ng\u00fcrmenin ne kadar zor oldu\u011funu. <em>S\u00fcrpriz de\u011feri<\/em> \\(\\log_b(1\/p_i)\\) ifadesinin beklenen de\u011feridir. Nadir olaylar \u015fa\u015f\u0131rt\u0131c\u0131d\u0131r (b\u00fcy\u00fck \\(\\log_b(1\/p_i)\\)) ama seyrek ger\u00e7ekle\u015fir; s\u0131k olaylar s\u0131k ger\u00e7ekle\u015fir ama pek \u015fa\u015f\u0131rtmaz. Entropi ikisinin dengesidir \u2014 olas\u0131l\u0131kla a\u011f\u0131rl\u0131kland\u0131r\u0131lm\u0131\u015f ortalama s\u00fcrpriz.<\/p>\n<p>H'nin de\u011feri 0 ile \\(\\log_b k\\) aras\u0131nda de\u011fi\u015fir. Bir sonu\u00e7 kesinse (tek bir \\(p_i = 1\\)) 0 olur; da\u011f\u0131l\u0131m d\u00fczg\u00fcn oldu\u011funda ise maksimumdur, \u00e7\u00fcnk\u00fc o zaman hi\u00e7bir tahmin di\u011ferinden daha iyi de\u011fildir. Taban 2 ile birim bit'tir ve H, sonucu belirlemek i\u00e7in gereken evet\/hay\u0131r sorular\u0131n\u0131n beklenen say\u0131s\u0131 olarak do\u011frudan okunabilir \u2014 veri s\u0131k\u0131\u015ft\u0131rma ve kodlama kuram\u0131n\u0131n ard\u0131ndaki fikir budur. Taban \\(e\\) ile birim nat't\u0131r; makine \u00f6\u011frenmesi ve fizikte yayg\u0131nd\u0131r. Taban 10 ise dit verir. Taban\u0131 de\u011fi\u015ftirmek yaln\u0131zca H'nin \u00f6l\u00e7e\u011fini de\u011fi\u015ftirir: da\u011f\u0131l\u0131mlar\u0131n s\u0131ralamas\u0131 ve \\(H\/H_{max}\\) oran\u0131 ayn\u0131 kal\u0131r.<\/p>\n<p><strong>Verimlilik<\/strong> \\(H\/H_{max}\\) (normalize edilmi\u015f entropi ya da g\u00f6reli entropi olarak da adland\u0131r\u0131l\u0131r), da\u011f\u0131l\u0131m\u0131n\u0131z\u0131n m\u00fcmk\u00fcn olan en belirsiz da\u011f\u0131l\u0131ma ne kadar yak\u0131n oldu\u011funu g\u00f6sterir. Yukar\u0131daki \u00f6rnekteki %92,32, d\u00f6rt markan\u0131n pazar\u0131 olduk\u00e7a dengeli payla\u015ft\u0131\u011f\u0131 anlam\u0131na gelir. 0'a yak\u0131n bir de\u011fer, sonucun neredeyse \u00f6ng\u00f6r\u00fclebilir oldu\u011fu anlam\u0131na gelir. Bu oran boyutsuz oldu\u011fundan, kategori say\u0131s\u0131 farkl\u0131 da\u011f\u0131l\u0131mlar aras\u0131nda belirsizli\u011fi kar\u015f\u0131la\u015ft\u0131rman\u0131n en pratik yoludur \u2014 ham H bunu ba\u015faramaz, \u00e7\u00fcnk\u00fc \\(H_{max}\\), \\(k\\) ile birlikte b\u00fcy\u00fcr.<\/p>\n<h2>Varsay\u0131mlar, S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Eksiksiz da\u011f\u0131l\u0131m:<\/strong> de\u011ferler t\u00fcm kategorileri kapsamal\u0131d\u0131r. Olas\u0131l\u0131klar\u0131n toplam\u0131 1 olmal\u0131d\u0131r (k\u00fc\u00e7\u00fck yuvarlama sapmalar\u0131 otomatik d\u00fczeltilir); say\u0131mlar ise toplamlar\u0131 1 olacak bi\u00e7imde normalize edilir.<\/li>\n<li><strong>S\u0131f\u0131r olas\u0131l\u0131klar:<\/strong> gelenek uyar\u0131nca \\(0 \\cdot \\log 0 = 0\\) kabul edilir; bu nedenle bo\u015f kategoriler hi\u00e7bir katk\u0131 yapmaz \u2014 ancak s\u0131f\u0131r olas\u0131l\u0131kl\u0131 bir kategorinin \\(k\\)'y\u0131 art\u0131rarak \\(H_{max}\\)'\u0131 y\u00fckseltti\u011fini, dolay\u0131s\u0131yla verimlili\u011finizi d\u00fc\u015f\u00fcrd\u00fc\u011f\u00fcn\u00fc unutmay\u0131n.<\/li>\n<li><strong>Kategoriler, b\u00fcy\u00fckl\u00fckler de\u011fil:<\/strong> entropi, <em>hangisi<\/em> kategorinin ger\u00e7ekle\u015fece\u011fine dair belirsizli\u011fi \u00f6l\u00e7er, de\u011ferlerin b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc de\u011fil. Kategori s\u0131ras\u0131n\u0131, aral\u0131klar\u0131n\u0131 ve etiketlerini yok sayar; bu y\u00fczden bir varyans \u00f6l\u00e7\u00fcs\u00fc de\u011fildir \u2014 bunun i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/carpiklik-ve-basiklik-hesaplama\/\">\u00c7arp\u0131kl\u0131k ve Bas\u0131kl\u0131k hesaplay\u0131c\u0131s\u0131na<\/a> bak\u0131n.<\/li>\n<li><strong>\u00d6rneklem verisi:<\/strong> k\u00fc\u00e7\u00fck \u00f6rneklemelerde say\u0131mlardan tahmin edilen entropi a\u015fa\u011f\u0131 do\u011fru yanl\u0131d\u0131r. Miller\u2013Madow yanl\u0131l\u0131k d\u00fczeltmesi, toplam say\u0131m \\(n\\) oldu\u011funda \\((k-1)\/(2n\\ln b)\\) kadar ekler \u2014 say\u0131mlar\u0131n\u0131z k\u00fc\u00e7\u00fckse uygulamaya de\u011fer.<\/li>\n<li><strong>\u0130lgili \u00f6l\u00e7\u00fcler:<\/strong> ayn\u0131 \\(p \\log p\\) terimleri, bir da\u011f\u0131l\u0131m\u0131 bir referans da\u011f\u0131l\u0131mla kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131lan \u00e7apraz entropi ve Kullback\u2013Leibler \u0131raksamas\u0131nda da yer al\u0131r. D\u00fczg\u00fcn bir yay\u0131l\u0131m\u0131n entropisi do\u011frudan <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/duzgun-dagilim-hesaplayici\/\">D\u00fczg\u00fcn Da\u011f\u0131l\u0131m ile<\/a> ili\u015fkilidir ve s\u0131n\u0131fland\u0131r\u0131c\u0131 belirsizli\u011fini de\u011ferlendirmek i\u00e7in d\u00fczenli olarak <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/karisiklik-matrisi-hesaplama\/\">karma\u015f\u0131kl\u0131k matrisine<\/a> uygulan\u0131r. G\u00f6zlemlenen bir da\u011f\u0131l\u0131m\u0131 beklenen bir da\u011f\u0131l\u0131mla kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/kruskal-wallis-testi-hesaplama\/\">Kruskal\u2013Wallis testi<\/a> de bir se\u00e7enektir.<\/li>\n<\/ul>\n<h2>H\u0131zl\u0131 Bak\u0131\u015f: Birimler ve Maksimum Entropi<\/h2>\n<table>\n<thead>\n<tr>\n<th>Taban<\/th>\n<th>Birim<\/th>\n<th>\\(k\\) kategori i\u00e7in \\(H_{max}\\)<\/th>\n<th>Tipik kullan\u0131m<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>2<\/td>\n<td>bit<\/td>\n<td>\\(\\log_2 k\\)<\/td>\n<td>Bilgi kuram\u0131, kodlama, bilgisayar bilimleri<\/td>\n<\/tr>\n<tr>\n<td>\\(e \\approx 2.718\\)<\/td>\n<td>nat<\/td>\n<td>\\(\\ln k\\)<\/td>\n<td>Makine \u00f6\u011frenmesi, istatistiksel mekanik<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>dit (hartley)<\/td>\n<td>\\(\\log_{10} k\\)<\/td>\n<td>Klasik bilgi \u00f6l\u00e7\u00fcleri<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Birimler aras\u0131nda d\u00f6n\u00fc\u015f\u00fcm i\u00e7in \\(H_{\\text{bit}} = H_{\\text{nat}} \/ \\ln 2\\) veya \\(H_{\\text{bit}} = H_{\\text{dit}} \\cdot \\log_2 10\\) ba\u011f\u0131nt\u0131lar\u0131n\u0131 kullan\u0131n. Hangi taban\u0131 se\u00e7ece\u011finizden emin de\u011filseniz 2 en g\u00fcvenli varsay\u0131land\u0131r \u2014 bit, en yayg\u0131n raporlanan birimdir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Herhangi bir olas\u0131l\u0131k ya da say\u0131m k\u00fcmesinin Shannon entropisini hesaplay\u0131n. Kategori ba\u015f\u0131na de\u011ferleri girin, bir logaritma taban\u0131 se\u00e7in (bit, nat veya dit) ve H de\u011ferini, maksimum entropiyi ve verimlilik oran\u0131n\u0131 al\u0131n.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[12],"tags":[64],"class_list":["post-4063","post","type-post","status-publish","format-standard","hentry","category-istatistik","tag-olasilik"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4063"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4063\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}