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A note on record times

Published online by Cambridge University Press:  14 July 2016

Mark Westcott
Mark Westcott*
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Canberra
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Abstract

This note indicates two alternative proofs for a result of Galambos and Seneta [1] on the distribution of ratios of successive record times in a sequence of independent and identically distributed random variables. Some consequences of one method of proof are discussed, and its analogues in a continuous time setting are described.

Keywords

RECORD TIMESRECORD HEIGHTSLIMIT LAWSSTIRLING NUMBERSPOINT PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 637 - 639
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Galambos, J. and Seneta, E. (1975) Record times. Proc. Amer. Math. Soc. 50, 383–387.CrossRefGoogle Scholar
[2] Gaver, D. P. (1976) Random record models. J. Appl. Prob. 13, 538–547.CrossRefGoogle Scholar
[3] Shorrock, R. W. (1972) On record values and record times. J. Appl. Prob. 9, 316–326.CrossRefGoogle Scholar
[4] Williams, D. (1973) On Rényi's ‘record’ problem and Engel's series. Bull. London Math. Soc. 5, 235–237 CrossRefGoogle Scholar
[5] Westcott, M. (1977) The random record model. Proc. R. Soc. London A. To appear.Google Scholar