Notes on Mathematical Statistics

The basis of actuarial science is statistical. For his raw material the actuary has tabulations of the behavior of certain statistics in the past. His task is to predict as accurately as possible the behavior of certain statistics in the future. If such future statistics have had identical counterparts in the past and if a large experience has been collected for these counterparts, the problem is relatively simple. The future will reproduce the past approximately. Unfortunately such an ideal condition seldom exists. Social, economic, and physical conditions change so that adjustments such as law amendment factors are necessary. Also, policy provisions and coverages change so that the statistic under study may not have existed in the past at all.