Estimating the Goodman, Keyfitz and Pullum Kinship Equations: An Alternative Procedure

Abstract

As is often the case in demography, Goodman et al. (Theoretical Population Biology, 5:1–27, 1974) developed their theory of the interrelationships of fertility, mortality and kinship numbers by means of continuous mathematics [integrals], but resorted to finite approximations for calculating results. Recent developments in computer software now provide an alternative procedure that avoids extensive programming of finite approximation algorithms: (1) continuous functions are found to represent discrete data on fertility and mortality; (2) the resulting functions and parameter estimates are then inserted directly into the kinship equations, and the integrals evaluated numerically. This procedure has the potential for use in many other areas of population mathematics, where theory is given by integrals and other continuous expressions, but data are for discrete age groups.