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Lookup NU author(s): Dr Jordan Stoyanov
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We present new results on the Hamburger moment problem for probability distributions and apply them to characterize the moment determinacy of powers and products of i.i.d. random variables with values in the whole real line. Detailed proofs of all results are given followed by comments and examples. We also provide new and more transparent proofs of a few known results. E.g., we give a new and short proof that the product of three or more i.i.d. normal random variables is moment-indeterminate. The illustrations involve specific distributions such as the double generalized gamma (DGG), normal, Laplace and logistic. We show that sometimes, but not always, the power and the product of i.i.d. random variables (of the same odd 'order') share the same moment determinacy property. This is true for the DGG and the logistic distributions.The paper also treats two unconventional types of problems: products of independent random variables of different types and a random power of a given random variable. In particular, we show that the product of Laplace and logistic random variables, the product of logistic and exponential random variables, the product of normal and chi(2) random variables, and the random power Z(N), where Z similar to N and N is a Poisson random variable, are all moment-indeterminate. (C) 2013 Elsevier B.V. All rights reserved.
Author(s): Stoyanov J, Lin GD, DasGupta A
Publication type: Article
Publication status: Published
Journal: Journal of Statistical Planning and Inference
Year: 2014
Volume: 154
Pages: 166-177
Print publication date: 01/11/2014
Online publication date: 16/11/2014
ISSN (print): 0378-3758
ISSN (electronic): 1873-1171
Publisher: Elsevier
URL: .http:/dx.doi.org/10.1016/j.jspi.2013.11.002
DOI: 10.1016/j.jspi.2013.11.002
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