On maximal sets of functions compatible with a partial ordering for distribution functions

Abstract

In this note we consider L-comparability of distribution functions as it is defined by D. Stoyan [6] and further considered by B. Lisek [2]. Especially, we give a complete answer to the question, proposed by Stoyan, for the structure of the set of L-ordering. This set is exactly the set of functions f:[0, ∞) → R ¹, which have a completely monotone first derivative on [0, ∞].