{"id":478,"date":"2015-01-06T16:23:06","date_gmt":"2015-01-06T16:23:06","guid":{"rendered":"http:\/\/frees.pajarel.net\/?page_id=478"},"modified":"2015-02-20T18:34:37","modified_gmt":"2015-02-21T00:34:37","slug":"3-multiple-decrement-tables","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/3-multiple-decrement-tables\/","title":{"rendered":"3. Multiple Decrement Tables"},"content":{"rendered":"<p>Tables of multiple decrement transition probabilities can be useful, particularly in discrete models. Because of the importance of multi-decrement applications, special notation is sometimes used. Here is common notation used in the US and Canada.<\/p>\n<p>Tables of multiple decrement transition probabilities can be useful, particularly in discrete models. Because of the importance of multi-decrement applications, special notation is sometimes used. Here is common notation used in the US and Canada.<\/p>\n<table>\n<tr>\n<td><\/td>\n<td colspan=\"2\">Notation<\/td>\n<\/tr>\n<tr>\n<td>Concept<\/td>\n<td>Multiple State<\/td>\n<td>Multi-Decrement<\/td>\n<\/tr>\n<tr>\n<td>Transition Probability<\/td>\n<td>\\(_t p_x^{0j}\\)<\/td>\n<td>\\(_t q_x^{(j)}\\)<\/td>\n<\/tr>\n<tr>\n<td>Total Transition Probability<\/td>\n<td>\\(_t p_x^{0\\bullet}\\)<\/td>\n<td>\\(_t q_x^{(\\tau)}\\)<\/td>\n<\/tr>\n<tr>\n<td>Survival Probability<\/td>\n<td>\\(_t p_x^{00}\\)<\/td>\n<td>\\(_t p_x^{(\\tau)}\\)<\/td>\n<\/tr>\n<tr>\n<td>Transition Forces<\/td>\n<td>\\(\\mu_{x+t}^{0j}\\)<\/td>\n<td>\\(\\mu_{x+t}^{(j)}=\\mu_{x}^{(j)}(t)\\)<\/td>\n<\/tr>\n<tr>\n<td>Total Transition Forces<\/td>\n<td>\\(\\mu_{x+t}^{0\\bullet}\\)<\/td>\n<td>\\(\\mu_{x+t}^{(\\tau)}=\\mu_{x}^{(\\tau)}(t)\\)<\/td>\n<\/tr>\n<\/table>\n<p><div class=\"alignleft\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/2-multiple-decrement-probabilities\/476-2\/\" title=\"Exercises\">&#9668 Previous page<\/a><\/div><div class=\"alignright\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/actuarial-mathematics\/multiple-decrement-models\/3-multiple-decrement-tables\/example-students-writing-actuarial-exams\/\" title=\"Example: Students Writing Actuarial Exams\">Next page &#9658<\/a><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tables of multiple decrement transition probabilities can be useful, particularly in discrete models. Because of the importance of multi-decrement applications, special notation is sometimes used. Here is common notation used in the US and Canada. &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-7I","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/478"}],"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=478"}],"version-history":[{"count":3,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/478\/revisions"}],"predecessor-version":[{"id":1608,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/478\/revisions\/1608"}],"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=478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}