The optimal gapped local alignment score of two random sequences follows a Gumbel distribution. The Gumbel distribution has two parameters, the scale parameter lambda and the pre-factor k. Presently, the basic local alignment search tool (BLAST) programs (BLASTP (BLAST for proteins), PSI-BLAST, etc.) use all time-consuming computer simulations to determine the Gumbel parameters. Because the sim...

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...

The widely-used hydrological procedures for calculating events with T-year return periods from data that follow a Gumbel distribution assume that the data sequence from which the Gumbel distribution is fitted remains stationary in time. If non-stationarity is suspected, whether as a consequence of changes in land-use practices or climate, it is common practice to test the significance of trend ...

The distribution of outliers is used as a tool for finding the extreme value distribution of meteorological parameters and to provide return values for large return periods from short records. Its potential is demonstrated for five cases. For extreme winds in the Northern Hemisphere (NH) the method shows that appropriately transformed annual maximum wind speeds can be described by a Gumbel dist...

In this paper, we consider a form of the generalized logistic distribution named symmetric extended generalized logistic distribution or extended type III generalized logistic distribution. The distribution is derived by compounding a two-parameter generalized Gumbel distribution with a two-parameter generalized gamma distribution. The cumulative distribution and some properties of this distrib...

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a nove...