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 for the distributions and convex constraints on
derivatives of their c.d.fs. 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 Tchebysheff type are derived by means
of general integral representation theorems. Some key words: Moment
sets, Tschebysheff inequalities, extremal bell-shaped distributions