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Determinacy of a distribution with finitely many mass points by finitely many moments

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  • Wei, Yixi
  • Ma, Jiang-Hong

Abstract

We consider the determinacy problem for a distribution function F(x), x∈R, by mixed data consisting of partial information given on F and knowing its finitely many moments. Necessary and sufficient conditions for solvability of the problem are derived. Essential is the established one-to-one correspondence between the Hamburger moment problem with finitely many moments and a discrete positive Borel measure concentrated at finitely many points on the real axis.

Suggested Citation

  • Wei, Yixi & Ma, Jiang-Hong, 2021. "Determinacy of a distribution with finitely many mass points by finitely many moments," Statistics & Probability Letters, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:stapro:v:176:y:2021:i:c:s0167715221000973
    DOI: 10.1016/j.spl.2021.109135
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    References listed on IDEAS

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    1. Gwo Dong Lin, 2017. "Recent developments on the moment problem," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    2. Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 85-90, August.
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