Winkler, Gerhard
(1998):
Moment Sets of Bell-Shaped Distributions: Extreme Points, Extremal Decomposition and Chebysheff Inequalities.
Collaborative Research Center 386, Discussion Paper 121
|
![[img]](https://epub.ub.uni-muenchen.de/1510/1.hassmallThumbnailVersion/paper_121.pdf)  Preview |
|
424kB |
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