Waitingtimes between record observations
- 1 November 1967
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 4 (1) , 206-208
- https://doi.org/10.2307/3212314
Abstract
If Δrdenotes the waitingtime between the (r− 1)st and therth upper record in a sequence of independent, identically distributed random variables with a continuous distribution, then it is shown that Δrsatisfies the weak law of large numbers and a central limit theorem.This theorem supplements those of Foster and Stuart and Rényi, who investigated the indexVrof therth upper record.Qualitatively the theorems establish the intuitive fact that for higher records, the waitingtime between the last two records outweighs even the total waitingtime for previous records. This explains also why the asymptotic normality of logVris very inadequate for approximation purposes—Barton and Mallows.Keywords
This publication has 3 references indexed in Scilit:
- Some Aspects of the Random SequenceThe Annals of Mathematical Statistics, 1965
- Distribution-Free Tests in Time-Series Based on the Breaking of RecordsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1954
- The Distribution and Frequency of Record ValuesJournal of the Royal Statistical Society Series B: Statistical Methodology, 1952