Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

M. S. Eliwa,Ziyad Ali Alhussain,M. El-Morshedy

doi:10.3390/math8030358

M. S. Eliwa, Ziyad Ali Alhussain + Show 1 more

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https://doi.org/10.3390/math8030358

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Abstract

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

Highlights

IntroductionThe Gompertz (Gz) distribution is a continuous probability distribution, named after Benjamin Gompertz
In probability and statistics, the Gompertz (Gz) distribution is a continuous probability distribution, named after Benjamin Gompertz
The assessment is based on a simulation study which is describes in the following: 2

Summary

Introduction

The Gompertz (Gz) distribution is a continuous probability distribution, named after Benjamin Gompertz. This distribution is a generalization of the exponential (Ex) distribution. The Gz distribution is often applied to describe the distribution of adult lifespans by demographers and actuaries. Related fields of science such as biology and gerontology consider the Gz distribution for the analysis of survival. Computer scientists have started to model the failure rates of computer codes using the Gz distribution. In marketing science, it has been used as an individual-level simulation for customer lifetime value modeling. See Willemse et al [1], Preston et al [2], Melnikov and Romaniuk [3], Ohishi et al [4], Bemmaor et al [5], Cordeiro et al [6], El-Bassiouny et al [7,8,9], Alzaatreh et al [10], Roozegar et al [11], Mazucheli et al [12], Eliwa et al [13], among others

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