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On characterizations of distributions via moments of record values
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  • Published: April 1987

On characterizations of distributions via moments of record values

  • G. D. Lin1 

Probability Theory and Related Fields volume 74, pages 479–483 (1987)Cite this article

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Summary

Let {X n } =1∞ n be a sequence of i.i.d. random variables having continuous distribution F(x) with E|X| l+ε<∞ for some positive integer l and for some ε>0. It is shown that for any fixed integer N≧0 the sequence of moments of record values {E(X L(n) )l} ∞ n=N characterizes F. Furthermore, this result is applied to the weak convergence of continuous distributions.

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Authors and Affiliations

  1. Institute of Statistics, Academia Sinica, 115, Taipei, Taiwan, Republic of China

    G. D. Lin

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  1. G. D. Lin
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Lin, G.D. On characterizations of distributions via moments of record values. Probab. Th. Rel. Fields 74, 479–483 (1987). https://doi.org/10.1007/BF00363510

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  • Received: 30 April 1985

  • Revised: 20 September 1986

  • Issue Date: April 1987

  • DOI: https://doi.org/10.1007/BF00363510

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Keywords

  • Positive Integer
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Weak Convergence
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