Waitingtimes between record observations

Author:

Neuts Marcel F.

Abstract

If Δr denotes the waitingtime between the (r − 1)st and the rth upper record in a sequence of independent, identically distributed random variables with a continuous distribution, then it is shown that Δr satisfies the weak law of large numbers and a central limit theorem.This theorem supplements those of Foster and Stuart and Rényi, who investigated the index Vr of the rth 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 logVr is very inadequate for approximation purposes—Barton and Mallows.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference5 articles.

1. The distribution and frequency of record values;Chandler;J.R. Statist. Soc.,1952

2. Some Aspects of the Random Sequence

3. Distribution-free tests in time series based on the breaking of records;Foster;J.R. Statist. Soc.,1954

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