Hostname: page-component-5b777bbd6c-7mr9c Total loading time: 0 Render date: 2025-06-20T15:57:19.703Z Has data issue: false hasContentIssue false
  • English
  • Français

On inference in a one-dimensional mosaic and an M/G/∞ queue

Published online by Cambridge University Press:  01 July 2016

Peter Hall
Peter Hall*
Affiliation:
The Australian National University
*
∗Postal address: Department of Statistics, Faculty of Economics, The Australian National University, GPO Box 4, Canberra ACT 2601, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose segments are distributed at random along a line, their locations being determined by a Poisson process. In the case where segment length is fixed, we compare efficiencies of several different estimates of Poisson intensity. The case of random segment length is also considered, and there we study estimation procedures based on empiric properties. The one-dimensional mosaic may be viewed as an M/G/∞ queue.

Keywords

CENTRAL LIMIT THEOREMCOVERAGE PROBLEMEFFICIENCYGEOMETRIC PROBABILITYM/G/∞QUEUEMOSAIC PROCESSPOISSON PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 1 , March 1985 , pp. 210 - 229
Copyright
Copyright © Applied Probability Trust 1985 

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

Bremaud, P. (1980) Point Processes and Queues. Springer-Verlag, New York.Google Scholar
Conolly, B. (1975) Queueing Systems. Ellis Horwood, Chichester.Google Scholar
Diggle, P. (1981) Binary mosaics and the spatial pattern of heather. Biometrics 37, 531–539.Google Scholar
Glaz, J. and Naus, J. (1979) Multiple coverage of the line. Ann. Prob. 7, 900–906.Google Scholar
Holst, L. (1980) On the lengths of the pieces of a stick broken at random. J. Appl. Prob. 17, 623–634.Google Scholar
Holst, L. (1981) On convergence of the coverage by random arcs on the circle and the largest spacing. Ann. Prob. 9, 648–655.Google Scholar
Hüsler, J. (1982) Random coverage of the circle and asymptotic distributions. J. Appl. Prob. 19, 578–587.Google Scholar
Janson, J. (1982) Random coverings of the circle with arcs of random length. In Essays in Honour of C. G. Esseen , ed. Gut, A. and Holst, L., Uppsala, Sweden, 62–73.Google Scholar
Roach, S. A. (1968) The Theory of Random Clumping. Methuen, London.Google Scholar
Siegel, A. F. (1978a) Random space filling and moments of coverage in geometrical probability. J. Appl. Prob. 15, 340–355.Google Scholar
Siegel, A. F. (1978b) Random arcs on the circle. J. Appl. Prob. 15, 774–789.CrossRefGoogle Scholar
Siegel, A. F. (1979) Asymptotic coverage distributions on the circle. Ann. Prob. 7, 651–661.Google Scholar
Siegel, A. F. and Holst, L. (1982) Covering the circle with random arcs of random sizes. J. Appl. Prob. 19, 373–381.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar