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

F. López-Blázquez () and B. Salamanca-Miño

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2013, vol. 22, issue 4, 715-738

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

Keywords: Record; δ-Records; Near-record; Distribution theory; Inter-record time; Maximum likelihood; 60G70; 60F15; 62F10 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:22:y:2013:i:4:p:715-738

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DOI: 10.1007/s11749-013-0340-8

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