Construction of multiple decrement tables under generalized fractional age assumptions

In this paper, we intend to develop a consistent methodology for constructing multiple decrement tables under generalized fractional age assumptions. Assuming that decrements have a common distribution at fractional ages, we derive conversion formulas to split or merge given multiple decrement tables in order to obtain a new multiple decrement table of interest. The assumptions that we consider are quite general, with a wide range of fractional age assumptions including the uniform distribution of decrements or the constant forces of decrement. Our proposed approaches allow us to directly obtain multiple decrement tables without the need for the associated single rates of decrement. They will also enable us to avoid potential inconsistency under the uniform distribution assumptions or unnaturalness arising from the constant forces assumption. In addition, as they navigate through a larger window, they will deepen our understanding of the classical results under the uniform distribution assumptions. Although our methodology is based on a common distribution function assumption, knowing the specific form of the function is unnecessary, since our conversion formulas do not depend upon it. Finally, numerical examples are illustrated where we investigate the main factors of the errors induced by the discrepancy between the true and assumed distributions. The numerical result shows that the relative errors under our approaches are practically negligible for moderate ranges of multiple decrement probabilities.