This article is cited in 27 papers

New checkable conditions for moment determinacy of probability distributions

J. M. Stoyanov^a, G. D. Lin^bc, P. Kopanov<sup>d

a</sup> Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
^b Social and Data Science Research Center, Hwa-Kang Xing-Ye Foundation, Taipei
^c Institute of Statistical Science, Academia Sinica, Taipei, Taiwan (Republic of China)
^d Faculty of Mathematics and Informatics, Plovdiv University "Paisii Hilendarski", Plovdiv, Bulgaria

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.

Keywords: probability distributions, moments, Stieltjes moment problem, Hamburger moment problem, Carleman's condition, Krein's condition, condition (L).

Received: 30.11.2018
Revised: 09.07.2019
Accepted: 18.07.2019

DOI: 10.4213/tvp5278

 English version: Theory of Probability and its Applications, 2020, 65:3, 497–509

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