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.
