On the Application of a Model of Mortality

Abstract

A mortality model was formulated by Mitra in 1983 from the pattern of the distribution of the force of mortality by age. The formulation of the functional relationship between a persons age resulted in his model equation with 3 parameters expressing as a linear function age. the upper limit of life and the probability of surviving from birth to a certain age. Encouraging results have been derived for both model and real life tables. In this model the number of unknown parameters was reduced from 3 to 2 by specifying value of infant mortality which is a meaningful identifier of a life table. The estimation of the parameters proved to be more efficient by the method of least squares with weights proportional to the reciprocals of the variances as the variances of the dependent variable vary with age. The model reproducers the given value of infant mortality. In this way estimates of the parameters were obtained from 52 life tables (26 for each sex) 13 from each of the 4 regions of Coale and Demenys regional model life tables which were selected to represent the entire range of mortality levels at uniform intervals. The estimated patterns of parameters obtained from these data sets demonstrated that 1 of the 2 parameters varies directly with life expectancy for both sexes while an inverse pattern is evident for the other with a turnaround at higher life expectancies. 2 important dimensions emerged that measure the level and the pattern of mortality. The double logarithmic model is capable of producing an infinite number of life tables while the regional tables are restricted by 4 regions. The goodness of fit of the double logarithmic model table can be improved by defining the 2 dimensions or by adding another dimension to it.