Properties and Applications of the Gompertz Distribution

Abstract

The importance of statistical distributions in describing and predicting real world events cannot be over-emphasized. The Gompertz distribution is one example of a widely-used distribution, with many applications to survival analysis. In this paper, several properties of the Gompertz distribution are studied. The two-parameter Gompertz distribution is shown to be identical to the three-parameter Gompertz exponential distribution. Functions used in reliability analysis related to the Gompertz distribution are reviewed. Properties of maximum likelihood estimate (MLE) parameter estimates for the Gompertz distribution are studied: the bias and root mean quared error of parameter estimates are expressed as a function of sample size and parameter values. When the Gompertz shape parameter is large, MLE parameter estimates may fail to exist because of parameter degeneracy, as the two-parameter Gompertz distribution approaches a 1-parameter exponential distribution. The distribution is fitted to real life data sets from both industrial and biological applications. Compared to several 3-parameter distributions, the Gompertz distribution provides significantly better fits to the industrial data sets chosen, but the 3-parameter generalized Gompertz distribution gives a better fit to guinea pig lifetime data