Copula Regression

Regression analysis is one of the most commonly used statistical methods. But in its basic form, ordinary least squares (OLS) is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the dependent variable may be non-normal. One approach that has been successful in overcoming these challenges is the generalized linear model (GLM), which requires that the dependent variable have a distribution from the exponential family. In this paper, we present copula regression as an alternative to OLS and GLM. The major advantage of a copula regression is that there are no restrictions on the probability distributions that can be used. In this paper, we will present the formulas and algorithms necessary for conducting a copula regression analysis using the normal copula. However, the ideas presented here can be used with any copula function that can incorporate multiple variables with varying degrees of association.

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