  General classes of bivariate distributions are well studied in literature.
Most of these classes are proposed via a copula formulation or extensions of
some characterisation properties in the univariate case. In Kundu(2022) we see
one such semi-parametric family useful to model bivariate data with ties. This
model is a general semi-parametric model with a baseline. In this paper we
present a characterisation property of this class of distributions in terms of
a functional equation. The general solution to this equation is explored.
Necessary and sufficient conditions under which the solution becomes a
bivariate distribution is investigated.
