On stochastic comparison of random vectors

Abstract

We provide sufficient conditions under which two random vectors could be stochastically compared using the standard construction. These conditions are weaker than those discussed by Arjas and Lehtonen (1978) and Veinott (1965). Using these conditions we present extensions of (i) a result of Block et al. (1984) concerning the stochastic monotonicity of independent and identically distributed random variables conditioned on their partial order statistics, and (ii) a theorem of Efron (1965) regarding an increasing property of Pólya frequency functions. Applications of these extensions are also pointed out.

Stochastic majorization of random variables by proportional equilibrium rates

“…We need the following increasing property of P61ya frequency functions (see Efron (1965) and Shanthikumar (1987)…”