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Method for constructing Stieltjes classes for M-indeterminate probability distributions

Lookup NU author(s): Dr Jordan Stoyanov, Dr Leonid Tolmatz

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Abstract

Let F be a distribution function with density f, finite moments of any positive integer order and such that the problem of moments for F has a nonunique solution (F is M-indeterminate). We are looking for explicit Stieltjes classes S = {fε = f[1 + εh], ε ∈ [-1, 1]} of distributions (here in terms of their densities) all sharing the same moments as those of F. We suggest a general method for constructing such classes. Then we apply our method to describe the M-indeterminacy of power transformations of popular distributions such as lognormal, inverse Gaussian and logistic. The Stieltjes classes presented here are new. We also find numerical values of the index of dissimilarity for some particular cases. © 2004 Elsevier Inc. All rights reserved.

Publication metadata

Author(s): Stoyanov J, Tolmatz L

Publication type: Article

Publication status: Published

Journal: Applied Mathematics and Computation

Year: 2005

Volume: 165

Issue: 3

Pages: 669-685

ISSN (print): 0096-3003

ISSN (electronic): 1873-5649

Publisher: Elsevier Inc.

URL: http://dx.doi.org/10.1016/j.amc.2004.04.035

DOI: 10.1016/j.amc.2004.04.035

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