Measures of distance between probability distributions

AbstractIn statistical estimation problems measures between probability distributions play significant roles. Hellinger coefficient, Jeffreys distance, Chernoff coefficient, directed divergence, and its symmetrization J-divergence are examples of such measures. Here these and like measures are characterized through a composition law and the sum form they possess. The functional equations f(pr, qs) + f(ps, qr) = (r + s)f(p, q) + (p + q)f(r, s) and f(pr, qs) + f(ps, qr) = f(p, q)f(r, s) are instrumental in their deduction