The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications

doi:10.1007/s42967-025-00503-4

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (4): 1324-1350.doi: 10.1007/s42967-025-00503-4

The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications

Sandra S. Ferreira^1,2, Dário Ferreira^1,2

1. Department of Mathematics, University of Beira Interior, Covilh?, 6200-768, Portugal;
2. Centre of Mathematics and Applications, University of Beira Interior, Covilh?, 6200-768, Portugal

收稿日期:2024-10-17 修回日期:2025-05-08 接受日期:2025-05-12 出版日期:2026-08-20 发布日期:2026-09-17
通讯作者: Sandra S. Ferreira, Email: sandraf@ubi.pt E-mail:sandraf@ubi.pt
基金资助:
Open access funding provided by FCT|FCCN (b-on). This work was partially supported by the Portuguese Foundation for Science and Technology through the projects: UIDP/MAT/00212/2020 and UIDP/MAT/00297/2020.

The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications

Sandra S. Ferreira^1,2, Dário Ferreira^1,2

1. Department of Mathematics, University of Beira Interior, Covilh?, 6200-768, Portugal;
2. Centre of Mathematics and Applications, University of Beira Interior, Covilh?, 6200-768, Portugal

Received:2024-10-17 Revised:2025-05-08 Accepted:2025-05-12 Online:2026-08-20 Published:2026-09-17
Supported by:
Open access funding provided by FCT|FCCN (b-on). This work was partially supported by the Portuguese Foundation for Science and Technology through the projects: UIDP/MAT/00212/2020 and UIDP/MAT/00297/2020.

摘要/Abstract

摘要： Various statistical properties of the exponentiated Weibull exponential (EWE) distribution including quantile and hazard rate functions, skewness, kurtosis, order statistics, and entropies are investigated. The parameters are estimated by the maximum likelihood estimation (MLE) method. The flexibility and behaviour of the estimators were studied through a simulation. The empirical flexibility of the presented distribution was examined by means of real-life data. It was observed that our distribution serves as a viable alternative model to existing probability densities in the literature for the analysis of lifetime data.

关键词: Maximum likelihood estimation (MLE), Moments, Orders statistics, Weibull distribution

Abstract: Various statistical properties of the exponentiated Weibull exponential (EWE) distribution including quantile and hazard rate functions, skewness, kurtosis, order statistics, and entropies are investigated. The parameters are estimated by the maximum likelihood estimation (MLE) method. The flexibility and behaviour of the estimators were studied through a simulation. The empirical flexibility of the presented distribution was examined by means of real-life data. It was observed that our distribution serves as a viable alternative model to existing probability densities in the literature for the analysis of lifetime data.

Key words: Maximum likelihood estimation (MLE), Moments, Orders statistics, Weibull distribution

Sandra S. Ferreira, Dário Ferreira. The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications[J]. Communications on Applied Mathematics and Computation, 2026, 8(4): 1324-1350.

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The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications

The Three-Parameter Exponentiated Weibull Exponential Distribution: Theoretical Properties and Practical Implications

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