Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-25T02:08:51.325Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterizations of exponential distributions by independent non-stationary record increments

Published online by Cambridge University Press:  14 July 2016

Dietmar Pfeifer
Dietmar Pfeifer*
Affiliation:
Technical University Aachen
*
∗Postal address: Institut für Statistik und Wirtschaftsmathematik, Rheinisch-Westfälische Technische Hochschule, Wüllnerstrasse 3, D-5100 Aachen, W. Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

A non-homogeneous version of the classical record process is presented which allows two different characterizations of exponential distributions by independent non-stationary record increments. A connection with the interarrival times of the corresponding record counting process (which is pure birth) is also pointed out.

Keywords

RECORD VALUESMARKOV ADDITIVE CHAINEXPONENTIAL DISTRIBUTIONINDEPENDENT NON-STATIONARY INCREMENTSCOUNTING PROCESSPURE BIRTH PROCESS
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 127 - 135
Copyright
Copyright © Applied Probability Trust 1982 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Biondini, R. W. and Siddiqui, M. M. (1975) Record values in Markov sequences. Proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes, Bloomington, July 31 — August 9, 1975. In Statistical Inference and Related Topics volume 2, Academic Press, New York, 291–352.Google Scholar
Breiman, L. (1968) Probability. Addison-Wesley, Reading, Mass.Google Scholar
Çinlar, E. (1972) Markov additive processes. I. Z. Wahrscheinlichkeitsth. 24, 85–93.Google Scholar
Deken, J. G. (1978) Scheduled maxima sequences. J. Appl. Prob. 15, 543–551.CrossRefGoogle Scholar
Gaver, D. P. (1976) Random record models. J. Appl. Prob. 13, 538–547.Google Scholar
Glick, N. (1978) Breaking records and breaking boards. Amer. Math. Monthly 85 (1), 2–26.Google Scholar
Guthrie, G. L. and Holmes, P. T. (1975) On record and inter-record times for a sequence of random variables defined on a Markov chain. Adv. Appl. Prob. 7, 195–214.Google Scholar
Shorrock, R. W. (1972) A limit theorem for inter-record times. J. Appl. Prob. 9, 219–223.Google Scholar
Tata, ?. N. (1969) On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitsth. 12, 9–20.Google Scholar
Westcott, M. (1977) The random record model. Proc. R. Soc. London A 356, 529–547.Google Scholar
Yang, M. C. K. (1975) On the distribution of inter-record times in an increasing population. J. Appl. Prob. 12, 148–154.Google Scholar