Complete convergence for widely orthant dependent random variables and its applications in autoregressive AR(1) models

The Frechet 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.