Moment Sets of Bell–Shaped Distributions: Extreme Points,Extremal Decomposition and Chebysheff Inequalities

The paper deals with sets of distributions which are given by moment conditions and convex constraints on derivatives of their cumulative distribution functions. A general albeit simple method for the study of their extremal structure, extremal decomposition and topological or measure theoretical properties is developed. Its power is demonstrated by the application to bell–shaped distributions. Extreme points of their moment sets are characterized completely (thus filling a gap in the previous theory) and inequalities of Chebysheff type are derived by means of general integral representation theorems.