The logarithmic skew-normal distributions are moment-indeterminate
Lin Gwo Dong and Stoyanov Jordan
Source: J. Appl. Probab. Volume 46, Number 3 (2009), 909-916.
Abstract
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.
Primary Subjects: 60E05
Secondary Subjects: 44A60
Keywords: Logarithmic skew-normal distribution; heavy tail; finite moments; problem of moments; nonuniqueness; Stieltjes class
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1253279858
Digital Object Identifier: doi:10.1239/jap/1253279858
Zentralblatt MATH identifier:
05611424
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