A recipe for bivariate copulas

ABSTRACT

We give conditions on a ? ?1, b ∈ ( ? ∞, ∞), and f and g so that C_{a, b}(x, y) = xy(1 + af(x)g(y))^b is a bivariate copula. Many well-known copulas are of this form, including the Ali–Mikhail–Haq Family, Huang–Kotz Family, Bairamov–Kotz Family, and Bekrizadeh–Parham–Zadkarmi Family. One result is that we produce an algorithm for producing such copulas. Another is a one-parameter family of copulas whose measures of concordance range from 0 to 1.