## Annals of Statistics

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

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

#### 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