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New Stieltjes classes involving generalized gamma distributions

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  • Stoyanov, Jordan
  • Tolmatz, Leonid
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    Abstract

    Let F be a distribution function with all moments finite and such that the problem of moments for F has a nonunique solution (F is M-indeterminate). Our goal is to explicitly describe a Stieltjes class S= f[var epsilon]=f[1+[var epsilon]h],[var epsilon][set membership, variant][-1,1] of distributions (here written in terms of the densities) all having the same moments as F. We study in detail the case when F is the distribution of the power transformation [xi]r,r>0 of a random variable [xi] with generalized gamma distribution. We derive new Stieltjes classes in this case and also for powers of the normal and the exponential distributions. We find the value of the index of dissimilarity for some of these classes.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 69 (2004)
    Issue (Month): 2 (August)
    Pages: 213-219

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    Handle: RePEc:eee:stapro:v:69:y:2004:i:2:p:213-219

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    Keywords: Problem of moments Stieltjes class of distributions Generalized gamma distribution Normal distribution Exponential distribution Index of dissimilarity;

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    Cited by:
    1. López-García, Marcos, 2009. "Characterization of solutions to the Stieltjes-Wigert moment problem," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1337-1342, May.

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