Stochastic orderings of convex/concave-type on an arbitrary grid

Several new classes of discrete stochastic orderings are introduced for com paring discrete random variables that are valued in an arbitrary ordered fi nite grid of nonnegative points. These order relations correspond to partic ular cases of integral stochastic orderings which are generated by differen t classes of functions of convex/concave-type defined on the grid. They are natural extensions from equidistant to arbitrary grids of various ordering s familiar in the literature. The main question addressed in the paper is h ow 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 p oint that is inserted in the grid.