CHARACTERIZATION OF PROBABILITY DISTRIBUTIONS BASED ON A GENERALIZED RAO-RUBIN CONDITION

SUMMARY. This paper presents a simple solution to the problem of characterzing the distribution of a non-degenerate, non-negative, integral valued Z, subjected to a destructive process when the damage model is binomial and when the Generalized Rao-Rubin condition holds true, namely, Pr(X = rl^) = Pr(X = r \ Y = 0, n2), 0 < nl9 n2 < 1, Z = X+F, X and Y are independent r.v.s.