A Novel Alpha Power Gumbel-X Family of Distributions with Exponential Baseline

Abstract

This study introduces the Novel Alpha Power Gumbel-X (NAPG-X) family of distributions, developed through the T-X transformation with a logarithmic generalizer. The NAPG-Exponential (NAPGEX) distribution is studied as a sub-model, with key mathematical properties derived, including the probability density function, cumulative distribution function, moments, moment generating function, Rényi entropy, and order statistics. The hazard rate function exhibits versatile shapes including increasing-decreasing, reversed-J, and L-shaped, making it suitable for diverse reliability applications. Ten classical estimation methods are evaluated through extensive Monte Carlo simulations across varying sample sizes and three parameter combinations. Results demonstrate that maximum likelihood and Anderson-Darling consistently provide superior performance with minimal bias, mean relative errors and root mean square errors. Furthermore, the practical applicability of the NAPGEX distribution is validated using three real-life datasets. Comprehensive comparisons using various performance measures reveal that the NAPGEX significantly outperforms competing models. These findings establish the NAPG-X family as a flexible and powerful tool for modeling asymmetric, positively skewed lifetime datasets across several scientific disciplines.