New Checkable Conditions for Moment Determinacy of Probability Distributions

Abstract

We have analyzed some conditions which are essentially involved in deciding whether or not a probability distribution is unique (moment-determinate) or nonunique (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 the Hamburger case (distributions on the whole real line) and the Stieltjes case (distributions on the positive half-line). Specific examples illustrate the results as well as the relationship between the new conditions and previously available conditions.