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Uncertainty Analysis Applications of The Generalized Diagonal Band Copula with Two-Sided Power Generating Densities Open Access

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This dissertation presents the development of a novel multivariate model based on copula dependence functions and common risk factors. Key accomplishments include procedures for fitting of model parameters to data, in addition to an efficient means of sampling from the resulting distribution. Copulas are an interesting result from the study of probability metric spaces that possess the ability of generating multivariate distributions coupled together from their univariate marginals. The work herein adds to the current copula literature, a new multivariate copula framework with reduced parameter estimation burden, by utilizing a common risk factor approach. Presently, there are only three broad categories of copula families that dominate in scholarly works: Elliptical copulas due to their familiarity in current statistical models (e.g. the Gaussian copula); Archimedean copulas due to their mathematical tractability; and Extreme Value copulas which are useful when the subject matter being studied is extreme valued. So, although the potential for the adoption of copulas in statistical analysis remains high, the actual implementation of copula models is often limited to these three copula families. Additionally, compared to bivariate copulas there is also a deficiency in the actual application of multivariate copula models. The current multivariate model is significant in that it offers an alternate multivariate copula model with a straightforward sampling procedure. The use of this model can aid in the further adoption of copulas in statistical dependence applications.

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