Generalized Inverse Xgamma Distribution: Properties, Estimation and Its Applications To Survival Data

Abstract

This article introduces a new form of IXGD called the generalized inverse Xgamma distribution. The proposed model exhibits the pattern of an inverted bathtub type hazard rate and it belongs to the family of positively skewed models. The explicit expressions of some distributional properties, such as, moments, inverse moments, conditional moments, mean deviation, quantile function etc. are derived. To estimate the unknown model parameters as well as survival characteristics, viz., survival function and hazard rate function, we used different estimation procedures, namely, method of maximum likelihood estimation, ordinary and weighted least squares estimation, Cramer-von-Mises estimation and maximum product of spacings estimation. Also, the Bayesian estimation of the same is studied with respect to the squared error loss function. The asymptotic confidence intervals and the Bayes credible intervals of the parameters are computed. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation in terms of average mean squared errors for the point estimates, average widths and coverage probabilities for interval estimates. Finally, the potential and practical applicability of the proposed model is illustrated through two real life examples. © 2025, Thai Statistical Association. All rights reserved.