{"id":488,"date":"2015-01-06T16:39:55","date_gmt":"2015-01-06T16:39:55","guid":{"rendered":"http:\/\/frees.pajarel.net\/?page_id=488"},"modified":"2015-02-20T18:38:42","modified_gmt":"2015-02-21T00:38:42","slug":"life-table-format","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/3-multiple-decrement-tables\/life-table-format\/","title":{"rendered":"Life Table Format"},"content":{"rendered":"<p>It is also common to display multi-decrement tables using a &#8220;life table&#8221; format. With the expected number of lives given by each status. To this end, let<\/p>\n<ul>\n<li>\\(x_0\\) be an initial age<\/li>\n<li>\\(l_{x_0}\\) be the expected number in state 0 (.e.g., &#8220;alive&#8221;) at age \\(x_0\\); this is the <em>radix<\/em> of the table<\/li>\n<li>\\(l_x\\) be the expected number in state 0 at age \\(x\\); this is computed as \\(l_x = l_{x_0} \\times ~_{x-x_0} p_{x_0}\\)<\/li>\n<li>\\( d_x^{(j)}\\) number of transitions from state 0 to state \\(j\\) (i.e., exits due to cause \\(j\\)), from ages \\(x\\) to \\(x+1\\).<\/li>\n<\/ul>\n<p>Here is an example of a quadruple decrement table where<\/p>\n<ul>\n<li>\\(j=0\\) means an active policyholder of a life insurance policy,<\/li>\n<li>\\(j=1\\) corresponds to death,<\/li>\n<li>\\(j=2\\) surrender of a life insurance policy, and<\/li>\n<li>\\(j=3\\) diagnosis of a critical illness.<\/li>\n<\/ul>\n<p><div class=\"alignleft\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/3-multiple-decrement-tables\/excerpt-from-a-critical-illness-multiple-decrement-table\/\" title=\"Excerpt from a Critical Illness Multiple Decrement Table\">&#9668 Previous page<\/a><\/div><div class=\"alignright\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/4-fractional-age-assumptions\/\" title=\"4. Fractional Age Assumptions\">Next page &#9658<\/a><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is also common to display multi-decrement tables using a &#8220;life table&#8221; format. With the expected number of lives given by each status. To this end, let \\(x_0\\) be an initial age \\(l_{x_0}\\) be the &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":478,"menu_order":2,"comment_status":"closed","ping_status":"open","template":"","meta":{"jetpack_post_was_ever_published":false},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8cLPd-7S","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/488"}],"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=488"}],"version-history":[{"count":3,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/488\/revisions"}],"predecessor-version":[{"id":755,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/488\/revisions\/755"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/478"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}