On the Construction of a Semiparametric Family of Bivariate Copulas Using the Opposite Diagonal Section of Copulas

In this article, a new semiparametric family of bivariate copulas is proposed and studied. The copulas of this family innovate in their construction; they are based on an original univariate generating function involving the opposite diagonal section of intermediary copulas. Several of their crucial properties are examined. In the practical part, we use them to estimate the reliability parameter in a stress-strength-dependent setting, including an estimation approach based on the Bernstein copula. Finally, their applicability and good performance are confirmed using a data set related to the logarithmic concentrations of two chemical elements in water samples.