The Exponentiated Fréchet Generator of Distributions with Applications

Abstract

In this article, we introduce the exponentiated Fréchet-G family of distributions. Several models of the introduced exponentiated Fréchet-G family are presented. The proposed family is precisely more flexible and effective in modeling complex data and is instrumental in reliability analysis. It covers a wide variety of shapes, such as unimodal, reverse J, right-skewed, symmetrical, and asymmetrical shapes. Various structural mathematical properties, such as the quantile, moment, incomplete moment, entropy, and order statistics, are derived. The parameters are evaluated using a parametric estimation method. The performance and flexibility of the exponentiated Fréchet-G family are analyzed via a simulation and two applications; one deals with reliability data, and the other deals with medical data.

Marshall-Olkin Exponentiated Fréchet Distribution

“…The Exponentiated Fréchet distribution has some appealing physical interpretations and shares many applications in extreme value theory such as supermarket queues, wind speeds, accelerated life testing, sea currents, earthquakes, horse racing, floods, track race records, and rainfall, among others [16].…”

Actuarial Measures, Regression, and Applications of Exponentiated Fréchet Loss Distribution

“…Due to its usefulness, several families of distributions have been developed for the generalization of the Fréchet distribution. Some of these include odd Fréchet family [4], extended odd Fréchet family [5,6], transmuted odd Fréchet family [7], generalized odd Fréchet [8], and exponentiated Fréchet family [9]. Speci cally, some generalizations of the Fréchet distribution include exponentiated Fréchet (EF) [10], beta Fréchet (BF) [11], gamma extended Fréchet [12], Kumaraswamy Fréchet (KF) [13], Weibull Fréchet [14], modi ed Fréchet [15], beta exponentiated Fréchet (BEF) [16], Burr X Fréchet [17], modi ed Kies-Fréchet [18], and extended Weibull Fréchet [19] distributions.…”

A New Generalization of the Exponentiated Fréchet Distribution with Applications

“…Several researchers proposed different extension of the Fréchet distribution in order to model different types of real life applications in all fields of study. Among these, the exponentiated Fréchet (EF) [28,29], the beta Fréchet [9], the gamma extended Fréchet [37], the Marshall-Olkin Fréchet (MO-F) [24], the transmuted exponentiated Fréchet (TEF) [17], the Kumaraswamy Fréchet [27], the Wiebull Fréchet [1], the odd Fréchet-G [19], the extended odd Fréchet-G [30], the Fréchet Topp Leone-G [34], the generalized transmuted Fréchet [36], the exponential transmuted Fréchet [35] and recently the exponentiated Fréchet-Lomax distributions [8].…”