Asian Journal of Probability and Statistics

This study introduces the Power Exp-Gamma (PEXPG) distribution by applying a power transformation to the Exp-Gamma model. The probability density and cumulative distribution functions are obtained, and selected statistical properties relevant to lifetime modelling are examined. These include raw moments and associated measures, the moment-generating, characteristic and cumulant-generating functions, order statistics, and the survival, hazard and reverse hazard functions. The density is also represented as a two-component mixture involving Weibull and generalised gamma distributions. The parameters are estimated by maximum likelihood, and the resulting likelihood equations are addressed iteratively using Fisher's scoring method in R. A simulation study considers three parameter combinations, sample sizes of 50, 100, 150 and 200, and 10,000 replications. The reported mean squared errors decrease with increasing sample size across the configurations examined. Model applicability is assessed using four datasets comprising annual maximum precipitation, breast cancer survival times, censored reliability failure times and recidivism failure times. The PEXPG model is compared with the power Akash, power Amarendra, power Ishita and power Sujatha distributions using the Akaike and Bayesian information criteria and the Kolmogorov–Smirnov statistic. The reported goodness-of-fit results favour PEXPG for all four datasets examined. The distribution also exhibits different hazard-rate patterns across parameter settings, indicating flexibility within the cases studied. These findings support further evaluation of PEXPG as an alternative model for the types of data considered.