Hausdorff moment problem: Reconstruction of distributions
AbstractThe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 78 (2008)
Issue (Month): 12 (September)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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, vol. 52(2), pages 215-230, June.
- Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 85-90, August.
- Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
- 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.
- Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
- 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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