Properties of the stochastic ordering for discrete distributions and their applications to the renewal sequence generated by a nonhomogeneous Markov chain
V. V. Golomozyĭ · Theory of Probability and Mathematical Statistics · 2019
The generalized stochastic ordering is studied for which the dominating sequence is not necessarily a probability distribution so that its total mass may exceed unity. We study the stochastic ordering for sums as well as random sums of independent as well as dependent random variables. A stochastic ordering is constructed for the renewal sequence generated by a nonhomogeneous Markov chain. The consideration is restricted to the case of discrete random variables.