Skip to main content
SpringerLink
Log in

Some statistical problems in random translations of stochastic point processes

  • Part II Inference For Stochastic Models
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

A random translation of a marked point process is considered. The distribution of random translation is assumed to be dependent upon the mark through a certain functionh(·). The main concern is to make inferences about the functionh(·) for different types of data. Complete identification and estimation are not possible in general, but some interesting particular solutions are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I.V. Basawa and B.L.S. Prakasa Rao,Statistical Inference for Stochastic Processes (Academic Press, 1980).

  2. D.R. Brillinger, Cross-spectral analysis of processes with stationary increments including the stationaryG/G/∞ queue, Ann. Prob. 2(1974)815.

    Google Scholar 

  3. M.L. Cleverson and J.V. Zidek, Bayes linear estimators of the intensity function of the nonstationary Poisson process, J. Amer. Statist. Assoc. 72, 357(1977)112.

    Google Scholar 

  4. D.R. Cox, Regression models and life-tables, J. Roy. Statist. Soc. B34(1972)187.

    Google Scholar 

  5. P.D. Feigin, A characterization of point processes with the order statistic property, Tech. Rep., Technion, Israel Institute of Technology (1977).

  6. C.D. Kemp and W.A. Kemp, Some properties of the Hermite distribution, Biometrika 52(1965)381.

    Google Scholar 

  7. D. König and K. Matthes, Verallgemeinerungen der Erlangser Formeln, I. Math. Nachr 26(1963)45.

    Google Scholar 

  8. T. Leonard, Density estimation, stochastic processes and prior information, J. Roy. Statist. Soc. B (1978)113.

    Google Scholar 

  9. J.S. Maritz,Empirical Bayes Methods (Methuen and Co. Ltd., 1970).

  10. N.M. Mirasol, The output of anM/G/∞ queueing system is Poisson, Oper. Res. 11(1963)282.

    Google Scholar 

  11. M. Neuts and S.I. Resnick, On the times of births in a linear birth process, J. Australian Math. Soc. XII(1971)473.

    Google Scholar 

  12. M.F. Ramalhoto, A classified bibliography of research on theG/G/∞ system (in preparation).

  13. H. Robbins, An empirical Bayes approach to statistics,3rd Berkeley Symp. on Math. Statistics and Probability 1 (University of California Press, 1956) p. 157.

  14. S.M. Ross, Identifiability inGI/G/K queues, J. Appl. Prob. 7, 3(1970)776.

    Google Scholar 

  15. D.L. Snyder,Random Point Processes (Wiley, New York, 1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1000, Lisboa, Portugal

    M. F. Ramalhoto

Authors
  1. M. F. Ramalhoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ramalhoto, M.F. Some statistical problems in random translations of stochastic point processes. Ann Oper Res 8, 229–242 (1987). https://doi.org/10.1007/BF02187094

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02187094

Keywords and phrases

Search

Navigation