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Hausdorff moment problem: Reconstruction of probability density functions


  • Mnatsakanov, Robert M.


The problem of recovering a moment-determinate probability density function (pdf) from its moments is studied. The proposed construction provides a method for recovery of different pdfs via simple transformations of the moment sequences. Uniform and L1-rates of convergence of moment-recovered pdfs are obtained. Finally, some applications and examples are briefly discussed.

Suggested Citation

  • Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1869-1877

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    References listed on IDEAS

    1. Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 85-90, August.
    2. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
    3. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
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    Cited by:

    1. repec:eee:apmaco:v:265:y:2015:i:c:p:225-236 is not listed on IDEAS
    2. Mnatsakanov, Robert M. & Li, Shengqiao, 2013. "The Radon transform inversion using moments," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 936-942.
    3. repec:eee:apmaco:v:268:y:2015:i:c:p:717-727 is not listed on IDEAS
    4. repec:eee:spapps:v:128:y:2018:i:1:p:132-155 is not listed on IDEAS
    5. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
    6. Mnatsakanov, Robert M., 2011. "Moment-recovered approximations of multivariate distributions: The Laplace transform inversion," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 1-7, January.

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