Distribution theory of $$\delta $$ δ -record values: case $$\delta \ge 0$$ δ ≥ 0

Fernando López-Blázquez () and Begoña Salamanca-Miño

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 24, issue 3, 558-582

Abstract: A $$\delta $$ δ -record of a sequence of random variables is an observation that exceeds the current record by $$\delta $$ δ units. This concept is relatively recent, so there are still many unknown aspects that require further research. In this work, for $$\delta \ge 0$$ δ ≥ 0 , we investigate the distribution theory of $$\delta $$ δ -record values from an iid sample from an absolutely continuous parent. We obtain recurrent expressions for the density function of $$\delta $$ δ -records and the probability mass function of inter- $$\delta $$ δ -record times. In the particular case of the exponential distribution, we show that the sequence of $$\delta $$ δ -records are distributed as the points of a (delayed) renewal process. Finally, we point out some applications of $$\delta $$ δ -records to paralyzable counters, blocks in automobile traffic, and queuing theory. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Records; Counting processes; Distribution theory; Exponential distributions; Type II particle counters; 60G70; 60F15; 62F10 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:24:y:2015:i:3:p:558-582

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DOI: 10.1007/s11749-014-0424-0

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