On the use of the truncated Gompertz distribution and other models to represent the parity progression functions of high fertility populations

Abstract

The Gompertz distribution, developed from the mortality “law”; long used by actuaries and demographers promises to be a useful distribution for many other demographic purposes as well. The continuous distribution can also be adapted to represent discrete data commonly encountered in demographic work, and maximum likelihood estimates of the two parameters are easily calculated using formulae developed in this paper, whether those data be continuous or discrete, truncated below or provided with observations in a final open‐ended interval. The distribution is unimodel. The use of the truncated form of the distribution, however, allows the researcher to fit it to a wider range of observed distributions, including many for which the density function is monotonic decreasing. Empirical studies using parity progression data of two high fertility populations indicate that the truncated Gompertz distribution in its discrete form provides a good overall picture of the parity distribution. Interestingly, the simple method of partial sums, commonly employed to fit the Gompertz function, appears to provide parameter estimates which are close to those estimated by maximum likelihood.