The Quasi Xgamma Distribution with Application in Bladder Cancer Data

Abstract

For the purpose of generalizing or extending an existing probability distribution, incorporation of additional parameter to it is very common in the statistical distribution theory and practice. In fact, in most of the times, such extensions provide better fit to the real life situations compared to the existing ones. In this article, we propose and study a two-parameter probability distribution, called quasi xgamma distribution, as an extension or generalization of xgamma distribution (Sen et al. 2016) for modeling lifetime data. Important distributional properties along with survival characteristics and distributions of order statistics are studied in detail. Method of maximum likelihood and method of moments are proposed and described for parameter estimation. A data generation algorithm is proposed supported by a Monte-Carlo simulation study to describe the mean square errors of estimates for different sample sizes. A bladder cancer survival data is used to illustrate the application and suitability of the proposed distribution as a potential survival model.