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We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail…
Chance constraints describe a set of given random inequalities depending on the decision vector satisfied with a large enough probability. They are widely used in decision making under uncertain data in many engineering problems. This paper…
A new class of copulas, termed the MGL copula class, is introduced. The new copula originates from extracting the dependence function of the multivariate generalized log-Moyal-gamma distribution whose marginals follow the univariate…
In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the important Frechet bounds the dependence structure…
When scholars study joint distributions of multiple variables, copulas are useful. However, if the variables are not linearly correlated with each other yet are still not independent, most of conventional copulas are not up to the task.…
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…
Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…
Copulas are functions that describe dependence structures of random vectors, without describing their univariate marginals. In statistics, the separation is sometimes useful, the quality and/or quantity of available information on these two…
In this paper we present a method for exact generation of multivariate samples with pre-specified marginal distributions and a given correlation matrix, based on a mixture of Fr\'echet-Hoeffding bounds and marginal products. The bivariate…
Consider the problem of drawing random variates $(X_1,\ldots,X_n)$ from a distribution where the marginal of each $X_i$ is specified, as well as the correlation between every pair $X_i$ and $X_j$. For given marginals, the…
Given $n$ symmetric Bernoulli variables, what can be said about their correlation matrix viewed as a vector? We show that the set of those vectors $R(\mathcal{B}_n)$ is a polytope and identify its vertices. Those extreme points correspond…
This paper develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
Copula models have become popular in different applications, including modeling shocks, in view of their ability to describe better the dependence concepts in stochastic systems. The class of maxmin copulas was recently introduced by…
This paper introduces a new discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent Bernoulli(p) trials needed in order to observe…
In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs.…
The present contribution derives an explicit expression for (a version of) every uni- and multi-variate conditional distribution (i.e., Markov kernel) of Archimedean copulas and uses this representation to generalize a recently established…