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Hausdorff moment problem: Reconstruction of distributions

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  • Mnatsakanov, Robert M.

Abstract

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

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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. 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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    1. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
    8. 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.

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