The McDonald Gompertz Distribution: Properties and Applications

TL;DR

This paper introduces the McDonald Gompertz distribution, a flexible five-parameter lifetime model with diverse failure rate shapes, extending several existing distributions and demonstrating its practical utility through real data applications.

Contribution

The paper presents a new five-parameter lifetime distribution extending multiple existing models, with detailed properties and real data applications.

Findings

The distribution can model various failure rate shapes.

Explicit formulas for moments, entropies, and quantiles are derived.

Application to real data shows its flexibility and usefulness.

Abstract

This paper introduces a five-parameter lifetime model with increasing, decreasing, upside -down bathtub and bathtub shaped failure rate called as the McDonald Gompertz (McG) distribution. This new distribution extend the Gompertz, generalized Gompertz, generalized exponential, beta Gompertz and Kumaraswamy Gompertz distributions, among several other models. We obtain several properties of the McG distribution including moments, entropies, quantile and generating functions. We provide the density function of the order statistics and their moments. The parameter estimation is based on the usual maximum likelihood approach. We also provide the observed information matrix and discuss inferences issues. In the end, the flexibility and usefulness of the new distribution is illustrated by means of application to two real data sets.