Construct a new family of bivariate copula

In statistics copulas study and their applications are growing field which are very efficient
functions in statistics and specially in statistical inference. Copula is used for constructing families of bivariate
and multivariate distributions and a way of studying measure of dependence structure also, this copula couple
multivariate distribution functions to their one-dimensional marginal distribution functions, which are
uniformly distributed in [0,1]. They are several methods for constructing copulas as inverse method,
Rüschendorf’s method, geometric method, algebraic method, and Archimedean method hence, we construct
new copula according to univariate function. Copulas have appeared in many important fields such as civil
engineering, biomedical studies, physics, quantitative finance, economics, climatology, social science, and
insurance risk management which confirms its importance. This paper introduces some bivariate copulas as
product, Clayton, Frank, Ali-Mikhail-Haq, Farlie-Gumbel-Morgensten, and Gumbel-Hougaard copulas. A
new class of bivariate copula is introduced which depending on a univariate function. The basic properties
which satisfied that is a true copula namely, the boundary conditions and the 2-increaing property are proved.
Several properties of this class are studied as concordance ordering, dependence, symmetry, and measures of
association. Further, example is proposed generated by a univariate function that described parametric family
of copula as product copula.