A Mixture of Clayton, Gumbel, and Frank Copulas: A Complete Dependence Model
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Date
2022
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Hindawi
Abstract
Knowledge of the dependence between random variables is necessary in the area of risk assessment and evaluation. Some of the
existing Archimedean copulas, namely the Clayton and the Gumbel copulas, allow for higher correlations on the extreme left and
right, respectively. In this study, we use the idea of convex combinations to build a hybrid Clayton–Gumbel–Frank copula that
provides all dependence scenarios from existing Archimedean copulas. (e corresponding density and conditional distribution
functions of the derived models for two random variables, as well as an estimator for the proportion parameter associated with the
proposed model, are also derived. (e results show that the proposed model is able to show any case of dependence by providing
coefficients for the upper tail and lower tail dependence.
Description
This article is published by Hindawi, 2022 and is also available at https://doi.org/10.1155/2022/1422394
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Citation
Hindawi Journal of Probability and Statistics Volume 2022, Article ID 1422394, 7 page