Enhancing Lifetime Data Modeling With the Modified Version of Weibull Distribution: A Comparative Approach

This study introduces a new two-parameter univariate distribution, a modified version of the Weibull distribution, for a non-negative realm. Originating from a framework introduced by Azzalini and Capitanio, the distribution exhibits a monotonically increasing hazard rate. It offers closed-form expressions for key statistical properties, including reliability functions, moments, moment-generating functions, and order statistics. An expression for random number generation is formulated. The maximum likelihood is employed for parameter inference. A simulation study shows the reliability of these estimators under various conditions. To assess the model's practical applicability, it is fitted to two real-world datasets: waiting times and tensile strength of carbon fiber. Results from quantile-quantile plots and validity tools tests show that the proposed model outperforms compared to selected alternatives, which shows its superior flexibility and accuracy to fit real-world problems.