{"id":28701,"date":"2013-05-21T17:18:16","date_gmt":"2013-05-21T11:48:16","guid":{"rendered":"http:\/\/www.kopykitab.com\/blog\/?p=28701"},"modified":"2013-05-21T17:18:16","modified_gmt":"2013-05-21T11:48:16","slug":"the-generalized-gamma-distribution-notes","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/the-generalized-gamma-distribution-notes\/","title":{"rendered":"The Generalized Gamma Distribution Notes"},"content":{"rendered":"<h1 style=\"text-align: center;\">The Generalized Gamma Distribution Notes<\/h1>\n<h3>The Generalized Gamma Distribution<\/h3>\n<p>Compared to the other distributions previously discussed, the generalized gamma distribution is not as frequently used for modeling life data;\u00a0however, it has the\u00a0the ability to mimic the attributes of other distributions, such as the Weibull or lognormal, based on the values of the distribution\u2019s parameters.\u00a0This\u00a0offers a compromise between two lifetime distributions. The generalized gamma function is a three-parameter distribution with parameters\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/7\/4\/b\/74b8eddf4b37de80c7c8eed1b64e46fc.png\">,\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/5\/b\/3\/5b33f39cef9df8c1d0386c99deb5c8d9.png\">\u00a0and\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/b\/5\/d\/b5d9e5a9ecd98ded0a1c6f439321904a.png\">. The\u00a0<i>pdf\u00a0<\/i>of the distribution is given by,<\/p>\n<dl>\n<dd>\n<dl>\n<dd><img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/3\/b\/7\/3b7278b36aef15371d54270f61f63214.png\"><\/dd>\n<\/dl>\n<\/dd>\n<\/dl>\n<p>where\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/2\/4\/b\/24b4737f4100228c545e66234e3de28a.png\">\u00a0is the gamma function, defined by:<\/p>\n<dl>\n<dd>\n<dl>\n<dd><img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/e\/e\/8\/ee86451431bf9e8f76c3d86c0ad3b206.png\"><\/dd>\n<\/dl>\n<\/dd>\n<\/dl>\n<p>This distribution behaves as do other distributions based on the values of the parameters. For example, if\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/6\/0\/2\/602aa81fe407ee5b3959f53f9f6e38ad.png\">, then the\u00a0distribution is identical to the Weibull distribution. If both\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/6\/0\/2\/602aa81fe407ee5b3959f53f9f6e38ad.png\">\u00a0and\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/7\/7\/c\/77c071d59ea999493bfda7e1e5724973.png\">, then the\u00a0distribution is identical to the exponential distribution, and for\u00a0<img alt=\"\" src=\"http:\/\/reliawiki.org\/images\/math\/1\/c\/e\/1ce5f9e0e28cbb07bc0d56dfcd824889.png\">\u00a0it is identical to the lognormal distribution. While the generalized gamma distribution is not often used to model life data by itself, its ability to behave like other more commonly-used life distributions is sometimes used to determine which of those life distributions should be used to model a particular set of data.<\/p>\n<p>The generalized gamma distribution and its characteristics are presented in\u00a0The Generalized Gamma Distribution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Generalized Gamma Distribution Notes The Generalized Gamma Distribution Compared to the other distributions previously discussed, the generalized gamma distribution is not as frequently used for modeling life data;\u00a0however, it has the\u00a0the ability to mimic the attributes of other distributions, such as the Weibull or lognormal, based on the values of the distribution\u2019s parameters.\u00a0This\u00a0offers a &#8230; <a title=\"The Generalized Gamma Distribution Notes\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/the-generalized-gamma-distribution-notes\/\" aria-label=\"More on The Generalized Gamma Distribution Notes\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[4773],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28701"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=28701"}],"version-history":[{"count":0,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/28701\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=28701"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=28701"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=28701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}