On the application of maximum entropy to the moments problem

Abstract

The use of the maximum entropy condition to obtain a solution to the moments problem, in which one seeks to reconstruct a function from the values of a finite set of its moments, is of interest in a variety of physical applications. Unfortunately, the standard analysis which is available, and on which these applications are based, takes as its starting point precise values of the moments whereas the physical applications involve imprecise data. In this paper it will be shown how to solve the moments problem, using the maximum entropy condition, starting from imprecise data values with errors specified by a χ2 -function.