GENERALIZED FRÉCHET MOMENT EXPONENTIAL DISTRIBUTION: MATHEMATICAL PROPERTIES, ESTIMATION, AND APPLICATIONS

Abstract

In this study, we introduced a new extension of the moment exponential distribution using the Fréchet family of distributions. The new model is named the “generalized Fréchet moment exponential (GFME) distribution”. We derived its mathematical properties, including moments, incomplete moments, probability weighted moments, moment generating function, entropies, quantile function, mean residual life, mean inactivity time, stress strength reliability, and order statistics. Moreover, the parameter estimation of the GFME distribution is discussed using the renowned maximum likelihood estimation and four distance-based approaches. A detailed Monte Carlo simulation study is utilized to illustrate the estimation behavior of the derived estimators using different sample sizes and choices of parameters. It is found that the bias and mean squared error are decreased with increasing sample sizes. The applicability and flexibility of the GFME distribution are illustrated using four asymmetric datasets from different fields. The proposed GFME model efficiently analyzed these datasets as compared to the considered renowned models, including other generalizations of the moment exponential distribution.