We introduce a new five-parameter distribution called the beta exponentiated Gumbel (BEG) distribution that includes the beta Gumbel, exponentiated Gumbel and Gumbel distribution. Expressions for the distribution function, density function and rth moment of the new distribution and order statistics are obtained. We discuss estimation of the parameters by maximum liklelihood ...

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. In this paper, we introduce a generalization—referred to as the beta Gumbel distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of this new distribution. We derive the analytical shapes of the correspond...

Abstract: The Exponentiated Gumbel (EG) distribution has been proposed to capture some aspects of the data that the Gumbel distribution fails to specify. In this paper, we estimate the EG's parameters in the Bayesian framework. We consider a 2-level hierarchical structure for prior distribution. As the posterior distributions do not admit a closed form, we do an approximated inference by using ...

The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of related methods, of which the Gumbel trick is one member, and show that the ne...

We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution Ga(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing a...

A class of univariate distributions called the exponentiated generalized class was recently proposed in the literature. A four-parameter model within this class named the exponentiated generalized Gumbel distribution is defined. We discuss the shapes of its density function and obtain explicit expressions for the ordinary moments, generating and quantile functions, mean deviations, Bonferroni a...