The extended Weibull–Fréchet distribution: properties, inference, and applications in medicine and engineering

Ekramy A. Hussein; Hassan M. Aljohani; Ahmed Z. Afify; Ekramy A. Hussein; Hassan M. Aljohani; Ahmed Z. Afify

doi:10.3934/math.2022014

AIMS Mathematics

2022, Volume 7, Issue 1: 225-246. doi: 10.3934/math.2022014

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Research article

The extended Weibull–Fréchet distribution: properties, inference, and applications in medicine and engineering

1.
Department of Statistics, Al-Azhar University, Nasr City 11651, Egypt
2.
Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
3.
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Received: 06 July 2021 Accepted: 17 September 2021 Published: 11 October 2021
MSC : 60E05, 62F10

In this paper, a flexible version of the Fréchet distribution called the extended Weibull–Fréchet (EWFr) distribution is proposed. Its failure rate has a decreasing shape, an increasing shape, and an upside-down bathtub shape. Its density function can be a symmetric shape, an asymmetric shape, a reversed-J shape and J shape. Some mathematical properties of the EWFr distribution are explored. The EWFr parameters are estimated using several frequentist estimation approaches. The performance of these methods is addressed using detailed simulations. Furthermore, the best approach for estimating the EWFr parameters is determined based on partial and overall ranks. Finally, the performance of the EWFr distribution is studied using two real-life datasets from the medicine and engineering sciences. The EWFr distribution provides a superior fit over other competing Fréchet distributions such as the exponentiated-Fréchet, beta-Fréchet, Lomax–Fréchet, and Kumaraswamy Marshall–Olkin Fréchet.
- Cramér–von Mises estimation,
- engineering data,
- extreme value distribution,
- Fréchet distribution,
- maximum product of spacing estimators,
- simulations
Citation: Ekramy A. Hussein, Hassan M. Aljohani, Ahmed Z. Afify. The extended Weibull–Fréchet distribution: properties, inference, and applications in medicine and engineering[J]. AIMS Mathematics, 2022, 7(1): 225-246. doi: 10.3934/math.2022014

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Abstract

In this paper, a flexible version of the Fréchet distribution called the extended Weibull–Fréchet (EWFr) distribution is proposed. Its failure rate has a decreasing shape, an increasing shape, and an upside-down bathtub shape. Its density function can be a symmetric shape, an asymmetric shape, a reversed-J shape and J shape. Some mathematical properties of the EWFr distribution are explored. The EWFr parameters are estimated using several frequentist estimation approaches. The performance of these methods is addressed using detailed simulations. Furthermore, the best approach for estimating the EWFr parameters is determined based on partial and overall ranks. Finally, the performance of the EWFr distribution is studied using two real-life datasets from the medicine and engineering sciences. The EWFr distribution provides a superior fit over other competing Fréchet distributions such as the exponentiated-Fréchet, beta-Fréchet, Lomax–Fréchet, and Kumaraswamy Marshall–Olkin Fréchet.

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