The exponentiated xgammma distribution: Estimation and its application

TL;DR

This paper introduces the exponentiated xgamma distribution (EXGD), a flexible lifetime model derived from a finite mixture of exponential and gamma distributions, with comprehensive properties and estimation methods.

Contribution

It presents a new lifetime distribution, EXGD, with detailed properties, multiple estimation techniques, and real data application, expanding the modeling options in reliability analysis.

Findings

The EXGD is highly flexible and positively skewed.

Various estimation methods effectively fit the model to data.

Application to medical data demonstrates practical utility.

Abstract

This article aims to introduced a new lifetime distribution named as exponentiated xgamma distribution (EXGD). The new generalization obtained from xgamma distribution, a special finite mixture of exponential and gamma distributions. The proposed model is very flexible and positively skewed. Different statistical properties of the proposed model, viz., reliability characteristics, moments, generating function, mean deviation, quantile function, conditional moments, order statistics, reliability curves and indices and random variate generation etc. have been derived. The estimation of the of the survival and hazard rate functions of the EXGD has been approached by different methods estimation, viz., moment estimate (ME),maximum likelihood estimate (MLE), ordinary least square and weighted least square estimates (LSE and WLSE), Cram\`er-von-Mises estimate (CME) and maximum product spacing estimate (MPSE). At last, one medical data set has been used to illustrate the applicability of the proposed model in real life scenario.