The Marshall-Olkin extended generalized Gompertz distribution

TL;DR

This paper introduces a new four-parameter distribution called the Marshall-Olkin extended generalized Gompertz distribution, detailing its properties, estimation methods, and application to real data.

Contribution

The paper presents a novel four-parameter distribution with flexible hazard functions and derives its mathematical properties, estimation techniques, and real-world applicability.

Findings

Flexible hazard rate shapes demonstrated

Mathematical properties derived and validated

Model successfully applied to real data

Abstract

A new four-parameter model called the Marshall-Olkin extended generalized Gompertz distribution is introduced. Its hazard rate function can be constant, increasing, decreasing, upside-down bathtub or bathtub-shaped depending on its parameters. Some mathematical properties of this model such as expansion for the density function, moments, moment generating function, quantile function, mean deviations, mean residual life, order statistics and R\'enyi entropy are derived. The maximum likelihood technique is used to estimate the unknown model parameters and the observed information matrix is determined. The applicability of the proposed model is shown by means of a real data set.