UNDERSTANDING RELATIONSHIPS USING COPULAS

UNDERSTANDING RELATIONSHIPS USING COPULAS

August 20, 1997 | Edward W. (Jed) Frees and Emiliano A. Valdez
This article introduces actuaries to the concept of "copulas," a tool for understanding relationships among multivariate outcomes. Copulas are functions that link univariate marginals to their full multivariate distribution. The authors explore practical applications of copulas, including estimation of joint life mortality and multidecrement models. They describe basic properties of copulas, their relationship to measures of dependence, and several families of copulas. The article also provides an annotated bibliography for further study and illustrates statistical inference procedures using insurance company data on losses and expenses. The methods are demonstrated through examples, such as fitting marginal distributions, fitting a copula to bivariate data, and using the bivariate fit to calculate reinsurance premiums and estimate regression functions. The article concludes with a discussion of additional applications of copulas, including stochastic ordering, fuzzy sets, and insurance pricing.This article introduces actuaries to the concept of "copulas," a tool for understanding relationships among multivariate outcomes. Copulas are functions that link univariate marginals to their full multivariate distribution. The authors explore practical applications of copulas, including estimation of joint life mortality and multidecrement models. They describe basic properties of copulas, their relationship to measures of dependence, and several families of copulas. The article also provides an annotated bibliography for further study and illustrates statistical inference procedures using insurance company data on losses and expenses. The methods are demonstrated through examples, such as fitting marginal distributions, fitting a copula to bivariate data, and using the bivariate fit to calculate reinsurance premiums and estimate regression functions. The article concludes with a discussion of additional applications of copulas, including stochastic ordering, fuzzy sets, and insurance pricing.
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