Copula Based Probabilistic Measures of Uncertainty with Applications
Pranesh Kumar
Mathematics and Statistics, University of Northern British Columbia, Prince George, BC, Canada

Uncertainty emerges when there is less information than the total information required to describe a system or environment. Uncertainty prevails in several forms and various kinds of uncertainties may arise from random fluctuations, incomplete information, imprecise perception, vagueness etc. We present a novel approach which considers information-theoretic measures and copula functions to characterize uncertainty associated with the probabilistic systems. Copula functions join uniform marginal distributions of random variables to form their multivariate distribution functions. Copulas are useful because they separate joint distributions into two contributions- (i) marginal distributions of each variable and (ii) copula as a measure of dependence. Several families of copulas with varying shapes and simulation programs are available providing flexibility in copula based modeling. We discuss the applications of Marshall-Olkin family of copulas based information measures to analyse uncertainty.

Keywords: Probabilistic uncertainty; Copulas; Information measures; Simulation

Biography: Dr. Pranesh Kumar is a Professor of Statistics at the Department of Mathematics & Statistics, University of Northern British Columbia, Canada. Dr. Kumar has research inetersts and has published in the areas of statistics, probability, econometrics, sample surveys, finance. He holds memberships in the international professional societies and the editorial boards of journals.