A simple graphical method for the comparison of two mortality experiences (Q2711703)

This paper is focused on the comparison of data for two different (age compatible) mortality experiences, either (1) to ascertain whether the same levels of mortality apply, or (2) to ascertain the likely nature of any significant difference between the mortality experiences. Typically the experiences may relate to two different policy durations in the same investigation, to the same investigation for two different observation periods, or to two different investigations. The examples of all three cases are presented. NEWLINENEWLINENEWLINEThis work is also intended to augment the conventional actuarial approach to mortality comparisons as described in Section 13 of \textit{D. O. Forfar, J. J. McCutcheon} and \textit{A. D. Wilkie} [J. Inst. Actuaries 115, 1-135 (1988)] and exemplified by the reports of the Continuous Mortality Investigation Bureau in the U.K., in-so-far as the first of these two objectives is concerned. This paper makes use of the differences in the logarithms of the crude mortality rates of the two experiences, matched age for age. Additionally, the approach leads naturally to the construction of a multiplicative age specific conversion factor linking the forces of mortality of the two mortality experiences involved. In addition, it is found that fitting cubic smoothing splines to such plots is particularly effective for targeting the underlying age specific pattern, much more so than lower-order polynomials in a number of the applications presented in the paper.