On conditions under which a probability distribution is uniquely determined by its moments
Probability
2019-12-03 v1
Abstract
We study the relationship between the well-known Carleman's condition guaranteeing that a probability distribution is uniquely determined by its moments, and a recent easily checkable condition on the rate of growth of the moments. We use asymptotic methods in theory of integrals and involve properties of the Lambert -function to show that the quadratic rate of growth of the ratios of consecutive moments, as a sufficient condition for uniqueness, is more restrictive than Carleman's condition. We derive a series of statements, one of them showing that Carleman's condition does not imply Hardy's condition, although the inverse implication is true. Related topics are also discussed.
Cite
@article{arxiv.1912.00160,
title = {On conditions under which a probability distribution is uniquely determined by its moments},
author = {Elena B. Yarovaya and Jordan M. Stoyanov and Konstantin K. Kostyashin},
journal= {arXiv preprint arXiv:1912.00160},
year = {2019}
}