Annals of Statistics

Sharp Upper Bounds for Probability on an Interval When the First Three Moments are Known

Morris Skibinsky

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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.

Article information

Source
Ann. Statist., Volume 4, Number 1 (1976), 187-213.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343353

Digital Object Identifier
doi:10.1214/aos/1176343353

Mathematical Reviews number (MathSciNet)
MR391221

Zentralblatt MATH identifier
0318.44010

JSTOR
links.jstor.org

Subjects
Primary: 44A50
Secondary: 62Q05: Statistical tables

Keywords
Barycentric coordinates closed subintervals indexed moment space partition moment function moment space normalized moment function sharp upper bound

Citation

Skibinsky, Morris. Sharp Upper Bounds for Probability on an Interval When the First Three Moments are Known. Ann. Statist. 4 (1976), no. 1, 187--213. doi:10.1214/aos/1176343353. https://projecteuclid.org/euclid.aos/1176343353


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