 The distributions of certain record statistics from a random number of observationsJ. A. Bunge and H. N. Nagaraja Stochastic Processes and their Applications, 1991, vol. 38, issue 1, 167-183 Abstract: Suppose we observe a random number N of independent identically distributed random variables in sequence. The record values are the successive maxima of this sequence. Assuming that N and the observations are independent, we obtain the joint distribution of the number of records and their values. Using this, the dependence structures of record values and interrecord counts are studied; this yields a necessary and sufficient condition for N to have geometric tail. In addition, we obtain the distribution of the number of records. When N is negative binomial, the expressions can be simplified; in one case the number of records has an exact Poisson distribution. Our results are applied to point process models considered by Gaver (1976) and Westcott (1977). Our results remain applicable when the assumption of identical distribution is relaxed to allow the distribution to change after a record event, as proposed by Pfeifer (1982). Keywords: random; record; model; record; values; number; of; records; interrecord; counts; point; processes; partial; fraction; expansion; geometric; distribution; negative; binomial; distribution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:38:y:1991:i:1:p:167-183 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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