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Copulas: Distribution Functions and Simulation

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International Encyclopedia of Statistical Science

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Introduction

In multivariate data modelling for an understanding of stochastic dependence the notion of correlation has been central. Although correlation is one of the omnipresent concepts in statistical theory, it is also one of the most misunderstood concepts. The confusion may arise from the literary meaning of the word to cover any notion of dependence. From mathematics point of view, correlation is only one particular measure of stochastic dependence. It is the canonical measure in the world of multivariate normal distributions and in general for spherical and elliptical distributions. However empirical research in many applications indicates that the distributions of the real world seldom belong to this class. We collect and present ideas of copula functions with applications in statistical probability distributions and simulation.

Dependence

We denote by (X, Y ) a pair of real-valued nondegenerate random variables with finite variances σ x 2 and σ y 2respectively. The...

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Author information

Authors and Affiliations

  1. University of Northern British Columbia, Prince George, BC, Canada

    Pranesh Kumar

Authors
  1. Pranesh Kumar
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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Kumar, P. (2011). Copulas: Distribution Functions and Simulation. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_191

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