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Hausdorff moment problem: Reconstruction of probability density functions

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  • Mnatsakanov, Robert M.

Abstract

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

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    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. Mnatsakanov, Robert M. & Li, Shengqiao, 2013. "The Radon transform inversion using moments," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 936-942.
    2. Ludovic Cal`es & Apostolos Chalkis & Ioannis Z. Emiris, 2021. "The cross-sectional distribution of portfolio returns and applications," Papers 2105.06573, arXiv.org.
    3. Calès, Ludovic & Chalkis, Apostolos & Emiris, Ioannis Z., 2019. "On the cross-sectional distribution of portfolio returns," JRC Working Papers in Economics and Finance 2019-11, Joint Research Centre, European Commission.
    4. Weimei Li & Leifu Gao, 2024. "Research on Risk-Averse Procurement Optimization of Emergency Supplies for Mine Thermodynamic Disasters," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    5. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
    6. Hansjörg Albrecher & José Carlos Araujo-Acuna, 2022. "On The Randomized Schmitter Problem," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 515-535, June.
    7. Gzyl, Henryk & Novi Inverardi, Pierluigi & Tagliani, Aldo, 2015. "Entropy and density approximation from Laplace transforms," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 225-236.
    8. Robert M. Mnatsakanov & Hansjoerg Albrecher & Stephane Loisel, 2022. "Approximations of Copulas via Transformed Moments," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3175-3193, December.
    9. Diel, Roland & Lerasle, Matthieu, 2018. "Non parametric estimation for random walks in random environment," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 132-155.
    10. Mnatsakanov, Robert M. & Pommeret, Denys, 2024. "On recovering the relative distribution, Part 1: The moment-recovered approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    11. Mnatsakanov, Robert M. & Sarkisian, Khachatur & Hakobyan, Artak, 2015. "Approximation of the ruin probability using the scaled Laplace transform inversion," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 717-727.
    12. 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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