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New Stieltjes classes involving generalized gamma distributions

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  • Stoyanov, Jordan
  • Tolmatz, Leonid

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.

Suggested Citation

  • Stoyanov, Jordan & Tolmatz, Leonid, 2004. "New Stieltjes classes involving generalized gamma distributions," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 213-219, August.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:2:p:213-219
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    Cited by:

    1. Gwo Dong Lin, 2017. "Recent developments on the moment problem," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    2. 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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