WAITINGTIMES BETWEEN RECORD OBSERVATIONS.
Abstract
If delta sub 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 delta sub r satisfies the weak law of large numbers and a central limit theorem. This theorems supplement those of Foster and Stuart and Renyi, who investigated the index V sub r 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 log V sub r is very inadequate for approximation purposes-Barton and Mallows. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1966
- Accession Number
- AD0635674
Entities
People
- Marcel F. Neuts
Organizations
- Purdue University