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On the moment problems


  • Gwo Dong Lin


Sufficient conditions for a distribution to be moment-indeterminate are investigated. By applying the fundamental results of Hardy theory, we give an alternative proof of Akhiezer's (1965) result concerning the moment-indeterminacy for distributions supported on the whole real line. Secondly, we give a simpler proof but still based on Slud (1993), for a result concerning distributions supported on the half-line (0, [infinity]). Besides, sufficient conditions for a distribution to be moment-determinate are also investigated.

Suggested Citation

  • Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 85-90, August.
  • Handle: RePEc:eee:stapro:v:35:y:1997:i:1:p:85-90

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    References listed on IDEAS

    1. Brands, J. J. A. M. & Steutel, F. W. & Wilms, R. J. G., 1994. "On the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 209-217, June.
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    Cited by:

    1. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
    2. Laura Mayoral, 2013. "Heterogeneous Dynamics, Aggregation, And The Persistence Of Economic Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 1295-1307, November.
    3. Ostrovska, Sofiya & Stoyanov, Jordan, 2010. "A new proof that the product of three or more exponential random variables is moment-indeterminate," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 792-796, May.
    4. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    5. repec:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0059-2 is not listed on IDEAS


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