Skip to main content
SpringerLink
Log in

Forecasting a class of doubly stochastic Poisson processes

  • Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

This paper deals with the doubly stochastic Poisson process (DSPP) with mean a truncated Gaussian distribution at any instant of time. The expression of its probability mass function is derived in this paper and it is also proved that the value of the process with maximum probability can be found in a known bounded interval. Furthermore, this paper also presents two methods to forecast the evolution of this kind of DSPP. The first one consists in modelling the mean process and then the probability mass function of the DSPP. The second method uses Multivariate Principal Component Regression to forecast the sample mean in the future instant and then the mass function. Both methods are applied to the real process of number of unpaid bank bills in Spain, forecasting the mass function of this process in 1997 and also its mode.

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

  • Aguilera, A.M., Ocaña, F.A. and Valderrama, M.J. (1999) ‘Forecasting time series by functional PCA. Discussion of several weighted approaches.’ Comp. Stat, 14, 443–467.

    Article  MATH  Google Scholar 

  • Cox, D.R. (1955) ‘Some Statistical Methods Connected with Series of Events’ J. Royal Statistical Society B. Vol. 17, 129–164.

    MATH  Google Scholar 

  • Jackson, J.E. (1991) A User’s Guide to Principal Components. Wiley,N. J.

    Book  MATH  Google Scholar 

  • Johnson, N.L. and Kotz, S. (1970) Continxious Univariate Distributions-I, Distributions in Statistics. Wiley, N. Y.

    Google Scholar 

  • Mittal, M.M. and Dahiya, R.C. (1987) ‘Estimating the parameters of a truncated Normal distribution.’, Communications in Statistics — Simulat., 16, 141–159.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Operations Research, Faculty of Pharmacy, University of Granada, Campus of Cartuja, 18071, Granada, Spain

    P. R. Bouzas & M. J. Valderrama

  2. Department of Statistics and Operations Research, Faculty of Sciences, University of Granada, Campus of Fuentenueva, 18071, Granada, Spain

    A. M. Aguilera

Authors
  1. P. R. Bouzas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Aguilera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. J. Valderrama
    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

Bouzas, P.R., Aguilera, A.M. & Valderrama, M.J. Forecasting a class of doubly stochastic Poisson processes. Statistical Papers 43, 507–523 (2002). https://doi.org/10.1007/s00362-002-0120-0

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-002-0120-0

Keywords

Search

Navigation