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Winkler, Gerhard (1998): Moment Sets of Bell-Shaped Distributions: Extreme Points, Extremal Decomposition and Chebysheff Inequalities. Collaborative Research Center 386, Discussion Paper 121




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