Moment Sets of Bell-Shaped Distributions: Extreme Points, Extremal Decomposition and Chebysheff Inequalities
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vor 26 Jahren
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
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
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