The extended Weibull-Frechet distribution: properties, inference, and applications in medicine and engineering

In this paper, a flexible version of the Frechet distribution called the extended Weibull-Frechet (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 Frechet distributions such as the exponentiated-Frechet, beta-Frechet, Lomax-Frechet, and Kumaraswamy Marshall-Olkin Frechet.

Automated summary

This paper proposes a flexible version of the Frechet distribution called the extended Weibull-Frechet (EWFr) distribution. The EWFr distribution exhibits various shapes of failure rate and density function, such as decreasing, increasing, upside-down bathtub, symmetric, asymmetric, reversed-J, and J shapes. The mathematical properties of the EWFr distribution are explored, and its parameters are estimated using different frequentist estimation approaches. The performance of these methods is evaluated through simulations, and the best approach for estimating the EWFr parameters is determined based on partial and overall ranks. Additionally, the superiority of the EWFr distribution over other competing Frechet distributions is demonstrated using real-life datasets from medicine and engineering sciences.