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On the moment problems

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  • Gwo Dong Lin

Abstract

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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    Citations

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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, 2009. "Heterogeneous dynamics, aggregation and the persistence of economic shocks," Working Papers 400, Barcelona School of Economics.
    3. Gaillac, Christophe & Gautier, Eric, 2021. "Non Parametric Classes for Identification in Random Coefficients Models when Regressors have Limited Variation," TSE Working Papers 21-1218, Toulouse School of Economics (TSE).
    4. Gwo Dong Lin & Jordan Stoyanov, 2015. "Moment Determinacy of Powers and Products of Nonnegative Random Variables," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1337-1353, December.
    5. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    6. Gwo Dong Lin, 2017. "Recent developments on the moment problem," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    7. Sander Muns, 2019. "An iterative algorithm to bound partial moments," Computational Statistics, Springer, vol. 34(1), pages 89-122, March.
    8. P. Patie & A. Vaidyanathan, 2022. "Non‐classical Tauberian and Abelian type criteria for the moment problem," Mathematische Nachrichten, Wiley Blackwell, vol. 295(5), pages 970-990, May.
    9. 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.
    10. Wei, Yixi & Ma, Jiang-Hong, 2021. "Determinacy of a distribution with finitely many mass points by finitely many moments," Statistics & Probability Letters, Elsevier, vol. 176(C).

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