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Hausdorff moment problem: Reconstruction of distributions


  • Mnatsakanov, Robert M.


The problem of approximation of the moment-determinate cumulative distribution function (cdf) from its moments is studied. This method of recovering an unknown distribution is natural in certain incomplete models like multiplicative-censoring or biased sampling when the moments of unobserved distributions are related in a simple way to the moments of an observed distribution. In this article some properties of the proposed construction are derived. The uniform and L1-rates of convergence of the approximated cdf to the target distribution are obtained.

Suggested Citation

  • Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1612-1618

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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. Bruce Lindsay & Ramani Pilla & Prasanta Basak, 2000. "Moment-Based Approximations of Distributions Using Mixtures: Theory and Applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 215-230, June.
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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. repec:eee:apmaco:v:268:y:2015:i:c:p:717-727 is not listed on IDEAS
    3. repec:eee:spapps:v:128:y:2018:i:1:p:132-155 is not listed on IDEAS
    4. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
    5. Gzyl, Henryk & Novi-Inverardi, Pier-Luigi & Tagliani, Aldo, 2013. "Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 457-463.
    6. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    7. 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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