PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

ESTIMATING THE WORKERS COMPENSATION TAIL 673TABLE D.1Sample q(x) ValuesCalendar YearAge 1970 1980 1990 2000 2020 2040 206020 .00175 .00156 .00130 .00110 .00091 .00078 .0006635 .00239 .00187 .00217 .00172 .00154 .00130 .0011050 .00861 .00685 .00556 .00496 .00397 .00330 .0027865 .02961 .02524 .02206 .01938 .01615 .01371 .0118280 .09386 .08308 .07604 .07028 .05929 .04976 .04261Six models of the number of PD claimants who would stillbe alive at the end of each future development year were derivedseparately for accident years 1975, 1980, 1985, 1990,1995, and 2000. Each of these models consists of a separatetwo-dimensional array, such as presented in Tables C.2.1 of AppendixC.The first step in deriving these arrays was to compile mortalityrates from the SSA tables. Table D.1 displays a sampling of theseq(x), or probability of death, values.Each of the one-year q(x) values was converted into survivalrates, denoted l(x), by taking the complement, yielding the ratiosin Table D.2.The entire array of resulting one-year l(x)s was then shifted sothat the rows of the original array became the diagonals of a newarray, that is, each successive column was shifted up one row.After the shift, the l(x)s were arranged as shown in Table D.3.Each row thus has a structure similar to an accident year reportingformat, as displayed in Table D.4.This shift facilitated multiplication of the survival ratios timesthe preceding number of surviving claimants for each age-atinjuryrow, working successively from left to right within eachage-at-injury row.