A family of fractional age assumptions

This paper introduces a unifying family of fractional age assumptions (FAAs) whose members include the familiar uniform distribution of deaths, constant force, and Balducci assumptions. The family also includes a wide range of alternative assumptions that can be used when those mentioned above are inappropriate. ombined with life table probabilities allow one to fully specify the age at death distribution. Traditionally, a single FAA is applied consistently across all ages. However, this frequently produces forces of mortality between integer ages that are inconsistent with the pattern of mortality rates across ages. In this paper, we introduce the idea that the FAA can be allowed to vary across ages so as to produce a more reasonable force of mortality function and more accurate actuarial present values. mily of FAAs is also considered in estimating mortality rates. Rather than making an arbitrary assumption in order to express probabilities and densities in terms of the mortality rate, we allow the data to determine the FAA.