This paper introduces the Type II Exponentiated Half-Logistic Exponential (TIIEHLEx) distribution, a three-parameter model designed for enhanced flexibility in modeling positive-valued data. We derive the distribution's core mathematical properties, including the probability density function, cumulative distribution function, and quantile function. A key focus of this work is the evaluation of fourteen non-Bayesian estimation methods to identify the most robust approach for parameter estimation. Through a comprehensive simulation study, we demonstrate that the Minimum Spacing Absolute Distance Estimator (MSADE) consistently outperforms other methods, yielding the lowest bias and mean square error across various sample sizes. The practical utility of the TIIEHLEx model is illustrated using March precipitation and insurance service exports data. Goodness-of-fit tests, including AIC and Kolmogorov-Smirnov statistics, reveal that the TIIEHLEx distribution provides a superior or highly competitive fit compared to several well-known heavy-tailed distributions, particularly in capturing complex hazard rate profiles.
Obulezi et al. (Mon,) studied this question.