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Lin’s condition for functions of random variables and moment determinacy of probability distributions

Lookup NU author(s): Dr Jordan Stoyanov

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This is the final published version of an article that has been published in its final definitive form by Academic Publishing House, 2017.

For re-use rights please refer to the publisher's terms and conditions.

Abstract

© 2017, Academic Publishing House. All rights reserved. If f = F′ is the density of a random variable X with distribution function F and f is positive and smooth, Lin’s condition is defined as follows: −xf′ (x)/f(x) ↗ ∞ as x → ∞. This condition is essentially involved, together with other conditions such as divergent Krein integral or fast growth rate of the moments, in deciding whether or not F is unique in terms of its moments (Mdeterminate) or non-unique (M-indeterminate). We analyze frequently used non-linear functional transformations of X and clarify whether or not Lin’s condition is preserved. Then we show that for a positive random variable X and any fixed integer n ≥ 2, the power Xn and the product X1…Xn of n independent copies of X, share the same moment-determinacy property.

Publication metadata

Author(s): Kopanov P, Stoyanov J

Publication type: Article

Publication status: Published

Journal: Comptes Rendus de L'Academie Bulgare des Sciences

Year: 2017

Volume: 70

Issue: 5

Pages: 611-618

Print publication date: 01/05/2017

Acceptance date: 08/01/2017

Date deposited: 04/08/2017

ISSN (print): 1310-1331

Publisher: Academic Publishing House

URL: http://www.proceedings.bas.bg/

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