New Checkable Conditions for Moment Determinacy of Probability Distributions

TL;DR

This paper introduces new, easily checkable conditions to determine whether a probability distribution is uniquely identified by its moments, extending existing results for both continuous and discrete distributions on the real line and positive half-line.

Contribution

It proposes novel conditions for moment determinacy applicable to both absolutely continuous and discrete distributions, enhancing the theoretical framework for identifying when distributions are uniquely determined by moments.

Findings

New conditions for moment determinacy introduced

Extended previous results in Hamburger and Stieltjes cases

Illustrative examples demonstrate the effectiveness of the conditions

Abstract

We have analyzed some conditions which are essentially involved in deciding whether or not a probability distribution is unique (moment-determinate) or non-unique (moment-indeterminate) by its moments. We suggest new conditions concerning both absolutely continuous and discrete distributions. By using the new conditions, which are easily checkable, we either establish new results, or extend previous ones in both Hamburger case (distributions on the whole real line) and Stieltjes case (distributions on the positive half-line). Specific examples illustrate both the results and the relationship between the new conditions and previously available conditions.