Comparing the Gompertz-Type Models with a First Passage Time Density Model

Abstract

In this paper we derive and analyse Gompertz type probability density functions and compare these functions to a first passage time density function. The resulting Gompertz type pdfs are mirror images of each other, each skewed in a specific direction, whereas the first passage type model gives functions with both left and right skeweness depending on parameter values. We apply these pdfs to the Life Table Data for females in the United States, 2004, and to the medfly data provided in Carey, 1992. Our application shows that the mortality data in the two cases have opposite skewness. The results support that the underlying mortality mechanism is qualitatively different in the cases.