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An additive property of weak records from geometric distributions

Author

Listed:
  • A. Castaño-Martínez
  • F. López-Blázquez
  • B. Salamanca-Miño

Abstract

Let $$\{W_m\}{_{m\ge 1}}$$ be the sequence of weak records from a discrete parent random variable, $$X$$ , supported on the non-negative integers. We obtain a new characterization of geometric distributions based on an additive property of weak records: $$X$$ follows a geometric distribution if and only if for certain integers, $$n,\, s\ge 1, W_{n+s}\stackrel{d}{=}W_n+W^{\prime }_s$$ , with $$W^{\prime }_s$$ independent of $$W_n$$ and $$W^{\prime }_s\stackrel{d}{=} W_s$$ . Copyright Springer-Verlag 2013

Suggested Citation

  • A. Castaño-Martínez & F. López-Blázquez & B. Salamanca-Miño, 2013. "An additive property of weak records from geometric distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 449-458, May.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:4:p:449-458
    DOI: 10.1007/s00184-012-0398-4
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    References listed on IDEAS

    as
    1. Katarzyna Danielak & Anna Dembińska, 2007. "Some characterizations of discrete distributions based on weak records," Statistical Papers, Springer, vol. 48(3), pages 479-489, September.
    2. Fernando López-Blázquez & Jack Wesołowski, 2001. "Discrete distributions for which the regression of the first record on the second is linear," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 121-131, June.
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