Journal Article

Statistical Inference for the Alpha Logarithmic Power Transformed Exponential Distribution With Applications

Chukwuma, Prince O., Jobarteh, Mustapha, Obiora‐Ilouno, Happiness O., Dike, Johnbosco C., Nejib Ouertani, Mohamed, Elgarhy, Mohammed, Obulezi, Okechukwu J., Hamdani, Hanene

2025

Overview

This research proposes and evaluates the effectiveness of the Alpha‐Logarithmic Power Transformed Exponential (ALPTE) distribution as a more general‐purpose, versatile lifetime distribution in comparison to conventional lifetime distributions. Bayesian and non‐Bayesian estimation were studied along with some properties of the ALPTE model, which were discussed. Mortality, Mobility, and Radiation datasets were analyzed and compared in a detailed manner. Data was evaluated using maximum likelihood estimation, descriptive statistics, and the goodness‐of‐fit tests such as AIC, BIC, CAIC, HQIC, Kolmogorov‐Smirnov, Anderson‐Darling, Cramér‐von Mises, and analyzed visually through model diagnostic plots such as boxplots, TTT plots, and P‐P plots. The ALPTE model consistently demonstrated superior performance over the Gamma, Lognormal, Gumbel, Weibull, and Exponential models across all datasets. It is remarkable how the ALPTE model not only enhanced the representation of light‐ and heavy‐tailed phenomena but also exhibited robustness to outliers alongside multiplicity in failure patterns, including increases, decreases, or constant rates. Estimates of ALPTE remained robust and interpretable even in the presence of data heterogeneity, particularly in large sample sizes. Such claims of flexibility and versatility further highlight the adaptability of the ALPTE distribution. The Alpha‐Logarithmic Power Transformed Exponential (ALPTE) distribution is introduced as a highly versatile lifetime model, demonstrating superior goodness‐of‐fit over common distributions (e.g., Gamma, Weibull) across diverse datasets. Its robust performance, even with data heterogeneity and outliers, showcases its adaptability for modeling various failure patterns and tail behaviors.

• Publisher: John Wiley & Sons, Inc,Wiley
• Subject: Alpha‐Log‐Power transformed exponential distribution / ALPT family / Bayesian analysis / COVID‐19 / Datasets / Electric power distribution / exponential distribution / Flexibility / Heterogeneity / Logarithms / Maximum likelihood estimation / Outliers (statistics) / Probability distribution functions / radiation data / Random variables / Statistical inference