Sharp Upper Bounds for Probability on an Interval When the First Three Moments are Known
The Annals of Statistics · 1976 · Volume 4 · Issue 1
Abstract
The subject of this research is the maximum probability assignable to closed subintervals of a closed, bounded, nondegenerate interval by distributions on that interval whose first three moments are specified. This maximum probability is explicitely displayed as a function of both the moments and the subintervals. The ready application of these results is illustrated by numerical examples.
Keywords
44A50, 62Q05, barycentric coordinates, closed subintervals, indexed moment space partition, moment function, moment space, normalized moment function, sharp upper bound
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