Related papers: Copula representations and order statistics for co…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
Dispersive order is a type of variability order for comparing the variability in probability distributions. Star order compares the skewness of probability distributions. This work considers dispersive and star orders of extreme order…
When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
The purpose of this paper is to characterize the concept of monotonicity according to a direction related to a set of n random variables in terms of its associated n-copula C. We start establishing relationships in the bivariate and…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. We introduce the concept of multivariate discrete copulas, discuss their equivalence to…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…
Regression analysis is one of the most popularly used statistical technique which only measures the direct effect of independent variables on dependent variable. Path analysis looks for both direct and indirect effects of independent…
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is…
Motivated by recently investigated results on dependence measures and robust risk models, this paper provides an overview of dependence properties of many well-known bivariate copula families, where the focus is on the Schur order for…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
An approach is proposed to determine structural shift in time-series assuming non-linear dependence of lagged values of dependent variable. Copulas are used to model non-linear dependence of time series components.
An extension of Archimax copula class in more than two random variables ( Multivariate ) was introduced in (J\'agr 2011) for describing dependency structures among random variables in higher dimension, and some properties of Archimax copula…
We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables $X$ and $Y$ given a random variable $Z$.…