Hausdorff moment problem: Reconstruction of distributions
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.
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Volume (Year): 78 (2008)
Issue (Month): 12 (September)
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References listed on IDEAS
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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;The Institute of Statistical Mathematics, 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.
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