New Class of Trivariate Copula: A Case Study for Water Quality Measurements

In this paper, we provide a new method to construct trivariate copula which generalizes a class of bivariate
copula. Based on the new method, two trivariate copulas are introduced using Product, Ali-Mikhail-Haq and FarlieGumbel-Morgenstern bivariate copulas. The selection of a bivariate copulas is adapted to make that the new trivariate
copula satisfy the mathematical properties of the copula. Some properties concerning dependence concepts of the two new
classes of trivariate copulas are discussed. Finally, an application for water quality measurements is presented to show
applicability of the proposed copulas. We compare the new trivariate copula to the trivariate nested hierarchical copula
using goodness-of-fit criteria to ensure that the proposed trivariate copula are the best fitted.