Gompertz - Power Series Distributions

TL;DR

This paper introduces the Gompertz-power series distribution, a flexible lifetime model encompassing several known distributions, with detailed properties, estimation methods, and a real-world application.

Contribution

It develops the Gompertz-power series distribution, analyzes its properties, and provides maximum likelihood estimation techniques including for censored data.

Findings

Distribution includes Gompertz-geometric, Gompertz-Poisson, and others.

Hazard rate can be increasing, decreasing, or bathtub-shaped.

Simulation studies validate the estimation procedures.

Abstract

In this paper, we introduce the Gompertz power series class of distributions which is obtained by compounding Gompertz and power series distributions. This distribution contains several lifetime models such as Gompertz-geometric, Gompertz-Poisson, Gompertz-binomial, and Gompertz-logarithmic distributions as special cases. Sub-models of the GPS distribution are studied in details. The hazard rate function of the GPS distribution can be increasing, decreasing, and bathtub-shaped. We obtain several properties of the GPS distribution such as its probability density function, and failure rate function, Shannon entropy, mean residual life function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented, and simulation studies are performed for evaluation of this estimation for complete data, and the MLE of parameters for censored data. At the end, a real example is given.