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The Extended Odd Fréchet Family of Distributions: Properties, Applications and Regression Modeling

Haitham M. Yosouf, Mahdi Rasekhi, Emrah Altun, Morad Alizadeh


The Fréchet distribution is an absolutely continuous distribution with wide applicability in extreme value theory. In this article, we introduce a new class of distributions called the extended odd Fr ´echet family with two extra positive shape parameters. We provide a comprehensive treatment of some of its mathematical properties. The maximum likelihood method is discussed to estimate the model parameters by means of a graphical Monte Carlo simulation study. The martingale and modified deviance residuals to detect outliers and evaluate the model assumptions are defined. We also introduce a new family of regression models based on the new family and demonstrate that the new log-location regression model can be very useful in analysing real data and provide more realistic fits than other regression models like the Log-Topp-Leone odd log-logistic-Weibull and the Log-Weibull models. The usefulness of the proposed models is illustrated by means of three real data sets.


Extended Fréchet, Maximum Likelihood Estimation, Monte Carlo simulation, Regression Model, Residual Analysis.

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