Stochastic Orderings of Convex/Concave-Type on an Arbitrary Grid

Several new classes of discrete stochastic orderings are introduced for comparing discrete random variables that are valued in an arbitrary ordered finite grid of nonnegative points. These order relations correspond to particular cases of integral stochastic orderings which are generated by different classes of functions of convex/concave-type defined on the grid. They are natural extensions from equidistant to arbitrary grids of various orderings familiar in the literature. The main question addressed in the paper is how an extension of the grid of points can affect such stochastic orderings. It will be shown that a crucial factor is the location of the additional point that is inserted in the grid.