Does Mccutcheon’s Mortality Polynomial Matrix Actually Account for Mortality Decline at Ten Years?

Abstract

This paper intends to employ a non-parametric technique as an alternative technique of modelling and estimating the instantaneous mortality rate intensities which serves as the underlying basis in modeling the distribution of future lifetime. It relies heavily on the analytic properties of life table survival functions l_x. The specific objectives of the study are (i) to derive models for the force of mortality using polynomial function (ii) to derive the survival function (iii) to detect the age at which mortality actually declines and (iv) estimate the curve of death. Computational evidence from our results confirms that in the models 1-3, the mortality intensity µ_x and the curve of death µ_xl_x are not both defined within the age band 0 ≤ x ≤ 2. The implication is that the infant mortality cannot be captured and the model is not admissible within this interval. Furthermore, it is also observed that µ_x = µ is constant within the interval 2 ≤ x ≤ 9 and mortality declines at age x=10. Consequently, there is a visible improvement in the care of infants which accounts for the decline in infant mortality. In model 4 since l_x < l_x-1 < l_x-2 < l_x-3 < l_x-4 < l_x-5 < l_x-6, it then becomes apparent that µ_x < 0. The fact that the force of mortality becomes negative represents a phantom detected from the McCutcheon's mortality matrix.