We describe and discuss the application of Gumbel statistics, which model extreme events, to WMAP 5-year measurements of the cosmic microwave background. We find that temperature extrema of the CMB are well modelled by the Gumbel formalism and describe tests for Gaussianity that the approach can provide. Comparison to simulations reveals Gumbel statistics to have only weak discriminatory power ...

This paper discusses the application of extreme events distribution taking the Limpopo River Basin at Xai-Xai station, in Mozambique, as a case analysis. We analyze the extreme value concepts, namely Gumbel, Fréchet, Weibull and Generalized Extreme Value Distributions and then extrapolate the original data to 1000, 5000 and 10000 figures for further simulations and we compare their outcomes bas...

In this paper, we study the estimation problems for the two-parameter exponentiated Gumbel distribution based on lower record values. An exact confidence interval and an exact joint confidence region for the parameters are constructed. A simulation study is conducted to study the performance of the proposed confidence interval and region. Finally, a numerical example with real data set is given...

Correspondence analysis is a multivariate technique used to visualize categorical data, usually data in a two-way contingency table. Some extensions of correspondence analysis to a continuous bivariate distribution are presented, rstly from a canonical correlation analysis perspective and then from a continuous scaling perspective. These extensions are applied to the Farlie-Gumbel-Morgenstern (...

We study the probability distribution of the pseudocritical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudocritical point and the extreme value statistics of random variables. For the Sherrington-Kirkpatrick model,...

Abstract This paper discusses how lognormal, Gumbel and log-Pearson type 3 distributions were eliminated as candidates for modelling at-site annual maximum discharge series in Bangladesh. Among candidate distributions, the generalized extreme value distribution best represented the statistical characteristics of observed data. Comparisons of distributions were based upon the root mean square de...