Unified (r, s)-entropy and its bivariate measures

There exist various generalizations of Shannon's entropy involving one and/or two real parameters. Some of these generalizations are written in a unified way that is called unified (r, s)-entropy. Joint and conditional unified (r, s)-entropy are defined for bivariate distributions. Some properties of these generalized entropies are studied. Also a pseudometric distance is defined and some of its properties are given.