In this paper, the Bayesian estimation of the parameters of mixture of two components of Gumbel type II distribution has been considered. A heterogeneous population has been modeled by means of two components mixture of the Gumbel type II distribution under type I censored data. The Bayes estimators of the said parameters have been derived under the assumption of informative priors using differ...

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...

Let X=(X1 ,X2 ) be a continuous random vector. Under the assumption that the marginal distributions of X1 and X2 are given, we develop models for vector X when there is partial information about the dependence structure between X1  and X2. The models which are obtained based on well-known Principle of Maximum Entropy are called the maximum entropy (ME) mo...

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimat...

We compute the limit shapes of the Young diagrams of the minimal difference p partitions and provide a simple physical interpretation for the limit shapes. We also calculate the asymptotic distribution of the largest part of the Young diagram and show that the scaled distribution has a Gumbel form for all p. This Gumbel statistics for the largest part remains unchanged even for general partitio...

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...

Recent events in financial markets have highlighted the frequency with which large scale financial losses occur. Extreme value theory focusses on the statistical properties of such extreme events. In this paper, extreme value distributions are applied in the context of option pricing. Analytic solutions to the standard European option problem based on the assumption that returns are Gumbel dist...

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...