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...

Computer-assisted sequence comparison has become an integral part of modern molecular biology. Two types of algorithms have been used: those which search for the optimal alignment (as exemplified by the Smith-Waterman algorithm [1]), and those which identify likely alignments (as exemplified by the HMM-based “Sequence Alignment Modules” [2]). In each case, the quality of alignment is summarized...

Recent theoretical studies of the adaptation of DNA sequences assume that the distribution of fitness effects among new beneficial mutations is exponential. This has been justified by using extreme value theory and, in particular, by assuming that the distribution of fitnesses belongs to the Gumbel domain of attraction. However, extreme value theory shows that two other domains of attraction ar...

This study proposes the use of the Gumbel logistic model, the bivariate extreme value distribution with Gumbel marginals, to analyze the joint distribution of annual maximum storm peaks (maximum rainfall intensities) and the corresponding storm amounts which are mutually correlated. Parameters of the distribution are estimated using the method of moments (MM). On the basis of the marginal distr...

[1] This paper shows how Gumbel-distributed data can be related to explanatory variables by using generalized linear models (GLMs) fitted by using a modified form of the iteratively weighted least squares algorithm (IWLS). Typical applications include (1) testing for trend in annual flood data, as a possible consequence of changing land cover or other factors; (2) testing for trend in annual ma...

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 ...

Consider a rowwise independent triangular array of gamma random variables with varying parameters. Under several different conditions on the shape parameter, we show that the sequence of row-maximums converges weakly after linear or power transformation. Depending on the parameter combinations, we obtain both Gumbel and non-Gumbel limits. The weak limits for maximum of the coordinates of certai...

The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem [1, 2, 3, 4]. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over continuous space. Central to the method is a stochastic process recently described in mathematical statistics that we call the Gumbel process. We presen...