A theorem of this paper proves that if the size distribution of random spheres is generalized gamma, its Wicksell transform and other related distributions belong to the domain of attraction of the Gumbel distribution. The theorem also shows the attraction coefficients of the distributions. The fatigue strength of high-strength steel is closely related to the maximum size of nonmetallic inclusi...

Generative Adversarial Networks (GAN) have limitations when the goal is to generate sequences of discrete elements. The reason for this is that samples from a distribution on discrete objects such as the multinomial are not differentiable with respect to the distribution parameters. This problem can be avoided by using the Gumbel-softmax distribution, which is a continuous approximation to a mu...

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...

The distribution of linear combinations of independent Gumbel random variables is of great interest for modeling risk and extremes in the most different areas of application. In this paper we develop near-exact approximations for the distribution of linear combination of independent Gumbel random variables based on a shifted generalized near-integer gamma distribution and on the distribution of...

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...

capacity of a road facility as an important characteristic in transportation and traffic studies is defined as the maximum rate of flow that could be held by that facility, which has been supposed to have a constant and certain value. this assumption, although necessary for most traffic studies, has also caused some problems, like that of demand exceeding capacity in many road facilities. resea...

In this paper we consider the Bayesian estimators for the unknown parameters of Gumbel type-II distribution. The Bayesian estimators cannot be obtained in closed forms. Approximate Bayesian estimators are computed using the idea of Lindley’s approximation under different loss functions. The approximate Bayes estimates obtained under the assumption of non-informative priors are compared with the...

In this paper, we propose a bivariate extension of univariate composite (two-spliced) distributions defined by Pareto distribution for values larger than some thresholds and Gumbel on the complementary domain. The purpose is to capture behavior data consisting mainly small medium but also extreme values. Some properties proposed are presented. Further, two estimation procedures discussed illust...