1967/04/01 by Marcel F. Neuts
Decision Sciences · Mathematics · Computer Science · #Probability and Risk Models #Stochastic processes and statistical mechanics #Bayesian Methods and Mixture Models
paper · doi:10.1017/s0021900200025377
If Δ r denotes the waitingtime between the ( r − 1)st and the r th 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 V r of the r th 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 log V r is very inadequate for approximation purposes—Barton and Mallows.