Related papers: A Discrete Gumbel Distribution
In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability…
We study the statistical distribution of the closest encounter between observations computed along different trajectories of a mixing dynamical system. At the limit of large trajectories, the distribution is of Gumbel type and depends on…
The proposed paper discusses the problem of discrimination between close hypotheses about distributions belonging to the Gumbel maximum domain of attraction. The distinctive feature of the proposed work is using only k higher order…
Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…
For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…
The Gumbel-Softmax probability distribution allows learning discrete tokens in generative learning, while the Gumbel-Argmax probability distribution is useful in learning discrete structures in discriminative learning. Despite the efforts…
The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and…
Recently, Lee and Cha (2015, `On two generalized classes of discrete bivariate distributions', {\it American Statistician}, 221 - 230) proposed two general classes of discrete bivariate distributions. They have discussed some general…
We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…
We show how convergence to the Gumbel distribution in an extreme value setting can be understood in an information-theoretic sense. We introduce a new type of score function which behaves well under the maximum operation, and which implies…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that,…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal gaps between…
The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape…
Weibull distribution is widely used in modelling health data. However, its lack of sufficient tail flexibility often results in poor fit in extreme events. We proposed another three-parameter extension of the Weibull distribution with…
We present evidence that the best model for empirical volume-price distributions is not always the same and it strongly depends in (i) the region of the volume-price spectrum that one wants to model and (ii) the period in time that is being…
Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Handling discrete latent variables is then challenging because the sampling process is not differentiable. Continuous…