Abstract
Abstract A large family of copulas with gamma components is examined, and interesting submodels are defined and analyzed. Parameter estimation is demonstrated for some of these submodels. A brief discussion of higher-dimensional versions is included.
Highlights
Arnold and Ng [3] introduced a bivariate second kind beta, or beta(2), distribution involving 8 independent random variables with gamma distributions
Note that after setting certain αj’s equal to zero, we must retain α + α + α >, α + α + α >, α + α + α >, and α + α + α >, in order to continue to have beta(2) marginal distributions. While this general bivariate beta model, and its submodels, have demonstrated exibility and usefulness in practice, the focus of this paper is on a speci c class of submodels of the beta(1) containing only copulas, that is, distributions with uniform marginals
Our gamma based copulas are obtained by setting the values of the parameters in the Arnold-Ng(8) bivariate beta distribution so that the marginals are Uniform(, )
Summary
Arnold and Ng [3] introduced a bivariate second kind beta, or beta(2), distribution involving 8 independent random variables with gamma distributions (subsequently such random variables will be referred to as gamma components). While this general bivariate beta model, and its submodels, have demonstrated exibility and usefulness in practice, the focus of this paper is on a speci c class of submodels of the beta(1) containing only copulas, that is, distributions with uniform marginals. Our gamma based copulas are obtained by setting the values of the parameters in the Arnold-Ng(8) bivariate beta distribution so that the marginals are Uniform( , ).
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