Abstract. This paper proposes a general non-Gaussian Ornstein-Uhlenbeck model for a joint financial process based on marginal Lévy measures joined by a Lévy copula. Simulated processes then result from choices of marginal measures and Lévy copulas, with resulting statistics and inferences. Selected for analysis are the 3/2-stable and Gamma marginal Lévy measures, along with Clayton, Gumbel, and...

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...

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...

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...

This paper constructs a new generalized multivariate version of the Gumbel copula that, to our knowledge, has not appeared in the statistical or mathematical literature.

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 Tracy-Widom distribution that has been much studied in recent years can be thought of as an extreme value distribution. We discuss interpolation between the classical extreme value distribution exp(− exp(−x)), the Gumbel distribution, and the Tracy-Widom distribution. There is a family of determinantal processes whose edge behaviour interpolates between a Poisson process with density exp(−x...