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.
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Acknowledgements
We would like to thank the referees for their quick and constructive comments. This research has been supported by Grant MTM2010-16949 of the Spanish Ministry of Education and Science and Grants FQM331, FQM5849 of Junta de Andalucía, Spain.
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López-Blázquez, F., Salamanca-Miño, B. Distribution theory of δ-record values. Case δ≤0. TEST 22, 715–738 (2013). https://doi.org/10.1007/s11749-013-0340-8
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DOI: https://doi.org/10.1007/s11749-013-0340-8