Skip to main content
SpringerLink
Log in

Statistical Analysis of a Spatial Counting Process Modelling Crystallization of Polymers

  • Published:
Statistical Inference for Stochastic Processes Aims and scope Submit manuscript

Abstract

The nucleation phase of the crystallization of polymers is described in terms of a stochastic spatial counting process, whose intensity depends upon the available volume. Estimation of the relevant parameters of the process are obtained via the maximum likelihood method [6]. The asymptotic properties of the estimators (proved in [6]) are applied to study their qualitative behaviour, as a function of the available volume and time. In this paper, a goodness of fit of the stochastic model proposed has been carried out via a Kolmogorov-Smirnov approach.

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. Aalen, O. O.: Non-parametric inference for a family of counting processes, Ann. Statist. 6(1978), 701–

    MATH  MathSciNet  Google Scholar 

  2. Allen, A. O.: Probability, Statistics and Queueing Theory, Computer Science and Applied Mathematics, Academic Press, New York, 1978.

    Google Scholar 

  3. Andersen, P. G., Borgan, Ø., Gill, R. D. and Keiding, N.: Statistical Models Based on Counting Processes, Springer-Verlag, Berlin, 1993.

    Google Scholar 

  4. Anderson, T. W.: The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc. 6(1955), 170–176.

    Article  MATH  MathSciNet  Google Scholar 

  5. Baddeley, A.: A limit theorem for statistics of spatial data, Adv. Appl. Probab. 12(1980), 447–461.

    Article  MATH  MathSciNet  Google Scholar 

  6. Capasso, V., De Giosa, M. and Mininni, R.: Asymptotic properties of the maximum likelihood estimators of parameters of a spatial counting process modelling crystallization of polymers, Stoch. Anal. Appl. 13(3) (1995), 279–294.

    MATH  MathSciNet  Google Scholar 

  7. Capasso, V. and Micheletti, A.: Simulation ofMultidimensional Stochastic ProcessesModelling Crystallization of Polymers., vol. 27/93, Q. Dip. Mat., Univ. Milano, 1993.

  8. Capasso, V., Micheletti, A., De Giosa, M. and Mininni, R.: Stochastic modelling and statistics of polymer crystallization processes, Surv. Math. Ind. 6(1996), 109–132.

    MATH  MathSciNet  Google Scholar 

  9. Fasano, A.: Modelling the Solidification of Polymers: an Example of ECMI Cooperation, ICIAM 91; R. E. O'Malley jr. (ed), Proc. Second Int. Conf. Ind. Appl. Math.SIAM, Philadelphia, pp. 99–118.

  10. Geurts, W. A. J., Hasselaar, M. M. A. and Verhagen, J. H.: Large Sample Theory for Statistical Inference in Several Software Reliability Models, Centre for Mathematics and Computer Science. Report MS-R8807, Amsterdam, 1988.

    Google Scholar 

  11. Micheletti, A. and Capasso, V.: The stochastic geometry of polymer crystallization processes, Stoch. Anal. Appl. 15(1997), 355–373.

    MATH  MathSciNet  Google Scholar 

  12. Rebolledo, R.: Sur les Applications de la Th´eorie des Martingales ´a l'Etude Statistique d'une Famille de Processus Ponctuels., Lecture Note in Mathematics, 636, Springer-Verlag, Berlin, 1978, pp. 27–70.

    Google Scholar 

Download references

Authors
  1. Rosa Maria Mininni
    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

Mininni, R.M. Statistical Analysis of a Spatial Counting Process Modelling Crystallization of Polymers. Statistical Inference for Stochastic Processes 2, 135–150 (1999). https://doi.org/10.1023/A:1009981714365

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009981714365

Search

Navigation