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- W2989698497 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 $W$-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." @default.
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- W2989698497 date "2019-11-30" @default.
- W2989698497 modified "2023-09-27" @default.
- W2989698497 title "On conditions under which a probability distribution is uniquely determined by its moments" @default.
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