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ARTICLE

Generalized Truncated Fréchet Generated Family Distributions and Their Applications

by Ramadan A. ZeinEldin^1,2, Christophe Chesneau^3,*, Farrukh Jamal⁴, Mohammed Elgarhy⁵, Abdullah M. Almarashi⁶, Sanaa Al-Marzouki⁶

1 Deanship of Scientific Research, King AbdulAziz University, Jeddah, 21589, Saudi Arabia
2 Faculty of Graduate Studies for Statistical Research, Cairo University, Al Orman, Giza Governorate, 12613, Egypt
3 Universit´e de Caen, LMNO, Campus II, Science 3, Caen, 14032, France
4 Department of Statistics, The Islamia University of Bahawalpur, Punjab, 63100, Pakistan
5 The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia, 31951, Egypt
6 Statistics Department, Faculty of Science, King AbdulAziz University, Jeddah, 21551, Saudi Arabia

* Corresponding Author: Christophe Chesneau. Email:

(This article belongs to the Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 126(2), 791-819. https://doi.org/10.32604/cmes.2021.012169

Received 16 June 2020; Accepted 16 October 2020; Issue published 21 January 2021

Abstract

Understanding a phenomenon from observed data requires contextual and efficient statistical models. Such models are based on probability distributions having sufficiently flexible statistical properties to adapt to a maximum of situations. Modern examples include the distributions of the truncated Fréchet generated family. In this paper, we go even further by introducing a more general family, based on a truncated version of the generalized Fréchet distribution. This generalization involves a new shape parameter modulating to the extreme some central and dispersion parameters, as well as the skewness and weight of the tails. We also investigate the main functions of the new family, stress-strength parameter, diverse functional series expansions, incomplete moments, various entropy measures, theoretical and practical parameters estimation, bivariate extensions through the use of copulas, and the estimation of the model parameters. By considering a special member of the family having the Weibull distribution as the parent, we fit two data sets of interest, one about waiting times and the other about precipitation. Solid statistical criteria attest that the proposed model is superior over other extended Weibull models, including the one derived to the former truncated Fréchet generated family.

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