{"id":458,"date":"2015-01-06T15:44:23","date_gmt":"2015-01-06T15:44:23","guid":{"rendered":"http:\/\/frees.pajarel.net\/?page_id=458"},"modified":"2015-02-20T18:25:59","modified_gmt":"2015-02-21T00:25:59","slug":"1-examples-of-multiple-decrement-models","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/1-examples-of-multiple-decrement-models\/","title":{"rendered":"1. Examples of Multiple Decrement Models"},"content":{"rendered":"<p>Multiple decrement models can be formulated as a special case of multiple state models. As with a multiple state model, we consider a life aged \\(x\\) who, at time point \\(t\\) (age \\(x+t\\)) is in one of \\(n+1\\) potential outcomes, (0,1, ldots, n). Specifically, we let \\(Y(t)\\) (sometimes denoted as \\(Y(x+t)\\) ) be a categorical random variable with potential outcomes (0,1, ldots, n).<\/p>\n<p>In a multiple decrement model, we start in state 0 but all other states are <em>absorbing states<\/em>, where it is not possible to leave.<br \/>\n<strong>Figure 1. Multidecrement Model as a MultiState Representation.<\/strong><br \/>\n<a href=\"http:\/\/www.ssc.wisc.edu\/~jfrees\/wp-content\/uploads\/2015\/01\/MultipleDecrement.png\"><img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/www.ssc.wisc.edu\/~jfrees\/wp-content\/uploads\/2015\/01\/MultipleDecrement-244x300.png\" alt=\"MultipleDecrement\" width=\"244\" height=\"300\" class=\"aligncenter size-medium wp-image-459\" srcset=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-content\/uploads\/2015\/01\/MultipleDecrement-244x300.png 244w, https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-content\/uploads\/2015\/01\/MultipleDecrement.png 315w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/a><br \/>\nBoth the &#8220;Alive-Dead&#8221; and the &#8220;Accidental Death&#8221; Models are special cases of multiple decrement models. For some other special cases, consider the following.<\/p>\n<p> <div class=\"alignleft\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/\" title=\"Multiple Decrement Models\">&#9668 Previous page<\/a><\/div><div class=\"alignright\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/1-examples-of-multiple-decrement-models\/special-case-1-cause-specific-death-model\/\" title=\"Special Case 1. Cause-Specific Death Model\">Next page &#9658<\/a><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Multiple decrement models can be formulated as a special case of multiple state models. As with a multiple state model, we consider a life aged \\(x\\) who, at time point \\(t\\) (age \\(x+t\\)) is in &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":454,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"jetpack_post_was_ever_published":false},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8cLPd-7o","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/458"}],"collection":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/comments?post=458"}],"version-history":[{"count":4,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/458\/revisions"}],"predecessor-version":[{"id":1596,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/458\/revisions\/1596"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/454"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}