Open Access
March, 1954 On the Reduced Moment Problem
Salem H. Khamis
Ann. Math. Statist. 25(1): 113-122 (March, 1954). DOI: 10.1214/aoms/1177728850

Abstract

For a special class of cumulative distribution functions which are solutions of a given reduced moment problem (cf. paragraph 3, pages 27 and 28, of [4]), the well known expression for the least upper bound of the absolute difference between any two solutions of the same reduced moment problem is improved upon by the introduction of a constant nonnegative multiplier which is smaller than unity in the case of the special class of solutions. Useful properties of the determinantal form of the classical expression for the least upper bound are derived. The numerical value of the constant multiplier is computed in the case of a well known class of cumulative distribution functions. In addition, a simple method is given for constructing, over a finite range, an infinite set of continuous and differentiable cumulative distribution functions which are solutions of the same reduced moment problem when one such solution is known. The new expression for the least upper bound, when applied to members of the constructed class of continuous solutions, may be helpful in deriving general, but crude, inequalities among orthogonal polynomials over a finite interval.

Citation

Download Citation

Salem H. Khamis. "On the Reduced Moment Problem." Ann. Math. Statist. 25 (1) 113 - 122, March, 1954. https://doi.org/10.1214/aoms/1177728850

Information

Published: March, 1954
First available in Project Euclid: 28 April 2007

zbMATH: 0055.33603
MathSciNet: MR59979
Digital Object Identifier: 10.1214/aoms/1177728850

Rights: Copyright © 1954 Institute of Mathematical Statistics

Vol.25 • No. 1 • March, 1954
Back to Top