Revision as of 11:10, 11 February 2026

Abstract

This study introduces the Truncated Modified Weighted Exponential (TrMWE) Distribution, developed by extending the traditional modified weighted exponential distribution with an additional parameter and truncating its support to a finite range, enhancing its adaptability for modeling lifetime and reliability data. The statistical properties of the TrMWE, including moments, the moment-generating function, the quantile function, and order statistics, are examined. Parameter estimation is performed via maximum likelihood estimation (MLE), least squares and weighted least squares methods, maximum product of spacing method, Cramer-Von-Mises method, Anderson-Darling method, and right and left tails Anderson-Darling methods, with analysis of the asymptotic behavior of the estimators. Rényi and Tsallis entropies are also derived to assess the distribution’s uncertainty. The practicality of the TrMWE is illustrated using three real datasets and compared with existing distributions based on goodness-of-fit criteria, such as the Akaike Information Criterion and Bayesian Information Criterion. The results highlight the distribution’s flexibility and superior performance in modeling complex datasets.OPEN ACCESS Received: 14/08/2025 Accepted: 05/11/2025 Published: 03/02/2026

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