The Transmuted Odd Fréchet-G Family of Distributions: Theory and Applications

Majdah M Badr,Ibrahim Elbatal,Farrukh Jamal,Christophe Chesneau,Mohammed Elgarhy

doi:10.3390/math8060958

Abstract

The last years, the odd Fréchet-G family has been considered with success in various statistical applications. This notoriety can be explained by its simple and flexible exponential-odd structure quite different to the other existing families, with the use of only one additional parameter. In counter part, some of its statistical properties suffer of a lack of adaptivity in the sense that they really depend on the choice of the baseline distribution. Hence, efforts have been made to relax this subjectivity by investigating extensions or generalizations of the odd transformation at the heart of the construction of this family, with the aim to reach new perspectives of applications as well. This study explores another possibility, based on the transformation of the whole cumulative distribution function of this family (while keeping the odd transformation intact), through the use of the quadratic rank transmutation that has proven itself in other contexts. We thus introduce and study a new family of flexible distributions called the transmuted odd Fréchet-G family. We show how the former odd Fréchet-G family is enriched by the proposed transformation through theoretical and practical results. We emphasize the special distribution based on the standard exponential distribution because of its desirable features for the statistical modeling. In particular, different kinds of monotonic and nonmonotonic shapes for the probability density and hazard rate functions are observed. Then, we show how the new family can be used in practice. We discuss in detail the parametric estimation of a special model, along with a simulation study. Practical data sets are handle with quite favorable results for the new modeling strategy.

Highlights

Nowadays, there is still a need for statistical models capable of extracting all the information from the data, in order to communicate on them and make them useful as well
We present some functions of the transmuted odd Fréchet-G (TOFr-G) family having several applications in probability and statistics
On the basis of the well-established transmuted-G and odd Fréchet-G families of distributions, we introduce a new family of distribution, called the transmuted odd Fréchet-G

Summary

Introduction

There is still a need for statistical models capable of extracting all the information from the data, in order to communicate on them and make them useful as well This is the case in engineering, economics, biological studies and environmental sciences. For this reason, several generations of statisticians have concentrated their efforts in improving the desirable properties of the probability distributions at the basis of these models, through various kinds of extensions or generalizations. Several generations of statisticians have concentrated their efforts in improving the desirable properties of the probability distributions at the basis of these models, through various kinds of extensions or generalizations In this regard, sophisticated mathematical modifications have emerged, with practical use encouraged by the modern informatics developments. New families of continuous distributions were proposed, including those developed in the following short list of references: [1,2,3,4,5,6,7,8,9,10]

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Conclusion