Sharp Upper Bounds for Probability on an Interval When the First Three Moments are Known
Morris Skibinsky · The Annals of Statistics · 1976
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.