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Exceedances of records

Author

Listed:
  • A. Castaño-Martínez

    (University of Cádiz)

  • F. López-Blázquez

    (University of Sevilla)

  • B. Salamanca-Miño

    (University of Sevilla)

Abstract

Given a sequence of random variables (rv’s) and a real function $$\psi $$ ψ , the $$\psi $$ ψ -exceedances form a subsequence consisting of those rv’s larger than a function, $$\psi $$ ψ , of the previous element of the subsequence. We present the basic distribution theory of $$\psi $$ ψ -exceedances for a sequence of independent and identically distributed rv’s. We give several examples and we study with more detail the case of exponential parents with $$\psi $$ ψ a linear function. The particular case of arithmetic exceedances is useful to describe the behavior of a type I counter when the arrival process of particles follows a non-homogeneous Poisson process. We also mention applications to destructive testing, early alert systems and the departure process of a $$M_t/D/1/1$$ M t / D / 1 / 1 queue.

Suggested Citation

  • A. Castaño-Martínez & F. López-Blázquez & B. Salamanca-Miño, 2016. "Exceedances of records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 837-866, October.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:7:d:10.1007_s00184-016-0580-1
    DOI: 10.1007/s00184-016-0580-1
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    References listed on IDEAS

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    1. Khmaladze, E. & Nadareishvili, M. & Nikabadze, A., 1997. "Asymptotic behaviour of a number of repeated records," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 49-58, August.
    2. Raúl Gouet & F. López & Gerardo Sanz, 2015. "On the point process of near-record values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 302-321, June.
    3. Eliazar, Iddo, 2005. "On geometric record times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 181-198.
    4. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
    Full references (including those not matched with items on IDEAS)

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