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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
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Abstract

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