Performance Rating of the Exponentiated Generalized Gompertz Makeham Distribution: An Analytical Approach

Ogunde Adebisi Ade

doi:10.11648/j.ajtas.20170605.12

Abstract

We developed a five parameter distribution known as the Generalized Exponentiated Gompertz Makeham distribution which is quite flexible and can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters making it more effective in modeling survival data and reliability problems. Some comprehensive properties of the new distribution, such as closed-form expressions for the density function, cumulative distribution function, hazard rate function, moment generating function and order Statistics were provided as well as maximum likelihood estimation of the Generalized Exponentiated Gompertz Makeham distribution parameters and at the end, in order to show the distribution flexibility, an application using a real data set was presented.

Highlights

Generalized Exponentiated Class of distribution Cordeiro G
A different version of Gompertz distribution which is called Gompertz Makeham (GM) distribution was introduced by another British actuary, Makeham
The GM family has been studied by Baily et al and an expression using the Lambert W function for the quantile function was given by Jodra, P

Summary

Introduction

Generalized Exponentiated Class of distribution Cordeiro G. M. et al Proposed a new method of adding two shape parameters to a continuous distribution that extends an idea which was first introduced by Lehmann and studied by Nadarajah and Kotz. The idea produces a new class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann alternatives. Given a continuous cumulative density function, G. M Cordeiro et al define the exponentiated generalized class of distribution by (1). Where are two additional shape parameters in equations can control the both the tail weight and possibly adding entropies to the center of the exponentiated generalized density function

Gompertz Makeham Distribution

The Proposed Generalized Exponentiated Gompertz Makeham Distributions

Investigation of the Asymptotic Properties of EEGM Distribution

Hazard Function

Generating Functions

Application