A New Exponentiated Power Distribution for Modeling Censored Data with Applications to Clinical and Reliability Studies

This paper suggests the Exponentiated Power Shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely the complete and incomplete moments, entropy, and moment generating function are derived and examined in a formal manner. Maximum likelihood estimation (MLE) techniques are used for estimation of parameters, as well as a Monte Carlo simulation study to account for estimator performance across varying sample sizes and parameter values. The EPS model is also generalized to a regression paradigm to include covariate data, whose estimation is also conducted via MLE. Practical utility and flexibility of the EPS distribution are demonstrated through two real examples: one for duration of repairs and another for HIV/AIDS mortality in Germany. Comparisons with some of the existing distributions, i.e., Power Zeghdoudi, Power Ishita, Power Prakaamy, and Logistic-Weibull, are made through some of the goodness-of-fit statistics such as log-likelihood, AIC, BIC, and Kolmogorov-Smirnov statistic. Graphical plots, including PP plots, QQ plots, TTT plots, and empirical CDFs, further confirm the high modeling capacity of the EPS distribution. Results confirm the high goodness-of-fit and flexibility of the EPS model, making it a very good tool for reliability and biomedical modeling.