Open Access

ARTICLE

A New Four-Parameter Moment Exponential Model with Applications to Lifetime Data

Abdullah Ali H. Ahmadini¹, Amal S. Hassan², Rokaya E. Mohamed^3,*, Shokrya S. Alshqaq⁴, Heba F. Nagy⁵
1 Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia
2 Faculty of Graduate Studies for Statistical Research, Department of Mathematical Statistics, Cairo University, Egypt
3 Sadat Academy for Management Sciences, Department of Mathematics, Statistics and Insurance, Cairo, Egypt
4 Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia
5 Faculty of Graduate Studies for Statistical Research, Department of Mathematical Statistics, Cairo University, Egypt
* Corresponding Author: Rokaya E. Mohamed. Email:
(This article belongs to this Special Issue: Recent Advances in Intelligent Systems and Communication)

Intelligent Automation & Soft Computing 2021, 29(1), 131-146. https://doi.org/10.32604/iasc.2021.017652

Received 01 February 2021; Accepted 06 March 2021; Issue published 12 May 2021

Abstract

In this research article, we propose and study a new model the so-called Marshal-Olkin Kumaraswamy moment exponential distribution. The new distribution contains the moment exponential distribution, exponentiated moment exponential distribution, Marshal Olkin moment exponential distribution and generalized exponentiated moment exponential distribution as special sub-models. Some significant properties are acquired such as expansion for the density function and explicit expressions for the moments, generating function, Bonferroni and Lorenz curves. The probabilistic definition of entropy as a measure of uncertainty called Shannon entropy is computed. Some of the numerical values of entropy for different parameters are given. The method of maximum likelihood is adopted for estimating the model parameters. We study the behavior of the maximum likelihood estimates for the model parameters using simulation study. A numerical study is performed to evaluate the behavior of the estimates with respect to their absolute biases, standard errors and mean square errors for different sample sizes and for different parameter values. Further, we conclude that the maximum likelihood estimates of the Marshal-Olkin Kumaraswamy moment exponential distribution perform well as the sample size increases. We take advantage of applied studies and offer two applications to real data sets that prove empirically the power of adjustment of the new model when compared to other lifetime distributions.

---

Keywords

Marshal-Olkin Kumaraswamy family; moment exponential distribution; quantile function; maximum likelihood estimation

---

Citations