Extended Type-II Topp-Leone Half-Logistic Distribution: Properties, Estimation, and Applications

Abstract

This study advances the Type II Topp-Leone half-logistic distribution by introducing a scale parameter, enhancing its flexibility and applicability to real-world datasets. We introduce this refined model as the extended Type II Topp-Leone half-logistic distribution and thoroughly derive its statistical properties, including the hazard function, reliability function, odds function, quantile function, order statistics, and entropy, providing a comprehensive theoretical framework. Parameter estimation was conducted using 16 diverse strategies, validated through extensive simulations across varying sample sizes and metrics, affirming the consistency of all estimates. Among these, the Kolmogorov method emerged as superior, demonstrating exceptional estimation accuracy and robustness. Applying the extended model to real-life datasets, specifically focusing on the failure times of repairable items in reliability engineering, revealed that it substantially outperformed existing models, as demonstrated by various performance metrics. This study offers a powerful and versatile tool for modelling complex phenomena in reliability engineering, enhancing maintenance scheduling and reliability assessments. The extended Type II Topp-Leone half-logistic distribution sets a new standard in reliability analysis, providing deeper insights and more reliable predictions for engineering applications.