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Distribution theory of δ-record values. Case δ≤0

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  • F. López-Blázquez
  • B. Salamanca-Miño

Abstract

We present the basic distribution theory of δ-record values, R n,δ , δ≤0, from a sequence of independent and identically distributed random variables from an absolutely continuous parent. We obtain recurrent formulas for the density function of R n,δ and a representation for this random variable that in some sense is similar to Tata’s representation for ordinary records. We also give the probability function of inter-δ-record times and some of its properties. We give examples of our results and also some elements of inference based on δ-records. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • F. López-Blázquez & B. Salamanca-Miño, 2013. "Distribution theory of δ-record values. Case δ≤0," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 715-738, November.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:4:p:715-738
    DOI: 10.1007/s11749-013-0340-8
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    References listed on IDEAS

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    1. Eliazar, Iddo, 2005. "On geometric record times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 181-198.
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    1. Fernando López-Blázquez & Begoña Salamanca-Miño, 2015. "Distribution theory of $$\delta $$ δ -record values: case $$\delta \ge 0$$ δ ≥ 0," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 558-582, September.
    2. 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.

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