Abstract
If Δ
r
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 Δ
r
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
Cited by
14 articles.
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