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The Logarithmic Skew-Normal Distributions are Moment-Indeterminate

Part of: Distribution theory - Probability Integral transforms, operational calculus

Published online by Cambridge University Press:  14 July 2016

Gwo Dong Lin  and
Jordan Stoyanov
Gwo Dong Lin*
Affiliation:
Academia Sinica, Taipei
Jordan Stoyanov*
Affiliation:
Newcastle University
*
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, Republic of China.
∗∗Postal address: School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK. Email address: jordan.stoyanov@ncl.ac.uk
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Abstract

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We study the class of logarithmic skew-normal (LSN) distributions. They have heavy tails; however, all their moments of positive integer orders are finite. We are interested in the problem of moments for such distributions. We show that the LSN distributions are all nonunique (moment-indeterminate). Moreover, we explicitly describe Stieltjes classes for some LSN distributions; they are families of infinitely many distributions, which are different but have the same moment sequence as a fixed LSN distribution.

Keywords

Logarithmic skew-normal distributionheavy tailfinite momentsproblem of momentsnonuniquenessStieltjes class

MSC classification

Secondary: 60E05: Distributions 44A60: Moment problems
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 3 , September 2009 , pp. 909 - 916
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

Dedicated to the memory of Professor Chris Heyde (1939-2008).

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