Hostname: page-component-cb9f654ff-mnl9s Total loading time: 0 Render date: 2025-08-19T22:11:06.004Z Has data issue: false hasContentIssue false
  • English
  • Français

Random displacements of regularly spaced events

Published online by Cambridge University Press:  14 July 2016

Roger B. Nelsen  and
Trevor Williams
Roger B. Nelsen
Affiliation:
Lewis and Clark College, Portland, Oregon
Trevor Williams
Affiliation:
University of Bristol
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the point process i + τi (i = 0, ± 1, ± 2, . . .), where the τi (assumed for convenience to be positive) are independent random samples from the same distribution. We define an inter-arrival interval as the stretch between neighbouring events, which need not belong to successive values of i, because of the jumbling of position occasioned by the variability of the τ. We obtain explicit expressions for the distribution of inter-arrival intervals in general, as well as the correlation coefficient between successive inter-arrival intervals in the case where the τ are exponentially distributed.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 183 - 195
Copyright
Copyright © Applied Probability Trust 

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.)

Article purchase

Temporarily unavailable

References

[1] Hardy, G. H. and Wright, E. M. (1938) An Introduction to the Theory of Numbers. Oxford Univ. Press, Oxford.Google Scholar
[2] Hobson, E. W. (1927) The Theory of Functions of a Real Variable and the Theory of Fourier's Series. Cambridge Univ. Press, Cambridge.Google Scholar
[3] Kendall, D. G. (1964) Some recent work and further problems in the theory of queues. Theor. Probability Appl. 9, 1–13.Google Scholar
[4] Lewis, T. (1961) The intervals between regular events displaced in time by independent random deviations of large dispersion. J. R. Statist. Soc. B 23, 476–483.Google Scholar
[5] Nelsen, R. B. and Williams, T. (1968) Randomly delayed appointment streams. Nature 219, 573–574.Google Scholar
[6] Winsten, C. B. (1959) Geometric distributions in the theory of queues. J. R. Statist. Soc. B 21, 1–35.Google Scholar