Generalized Gompertz-power series distributions

TL;DR

This paper introduces a new class of lifetime distributions by combining generalized Gompertz and power series distributions, providing flexible hazard functions and deriving key properties and estimation methods.

Contribution

It proposes the generalized Gompertz-power series distribution, extending lifetime models with diverse hazard shapes and detailed statistical properties and estimation procedures.

Findings

Distribution includes several lifetime models as special cases.

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

Maximum likelihood estimation via EM-algorithm is developed.

Abstract

In this paper, we introduce the generalized Gompertz-power series class of distributions which is obtained by compounding generalized Gompertz and power series distributions. This compounding procedure follows same way that was previously carried out by Silva et al. (2013) and Barreto-Souza et al. (2011) in introducing the compound class of extended Weibull-power series distribution and the Weibull-geometric distribution, respectively. This distribution contains several lifetime models such as generalized Gompertz, generalized Gompertz-geometric, generalized Gompertz-poisson, generalized Gompertz-binomial distribution, and generalized Gompertz-logarithmic distribution as special cases. The hazard rate function of the new class of distributions can be increasing, decreasing and bathtub-shaped. We obtain several properties of this distribution such as its probability density function, Shannon entropy, its mean residual life and failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented, and sub-models of the distribution are studied in details.