A recipe for bivariate copulas
ABSTRACT We give conditions on a ⩾ −1, b ∈ ( − ∞, ∞), and f and g so that Ca, 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.