Testing a homogeneity of stochastic processes

Jaromír Antoch; Daniela Jarušková

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 415-430
  • ISSN: 0023-5954

Abstract

top
The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests for a detection of a change in an intensity of the Poisson process are described and illustrated by an example. We cover both the case when the time of the change is assumed to be known or unknown.

How to cite

top

Antoch, Jaromír, and Jarušková, Daniela. "Testing a homogeneity of stochastic processes." Kybernetika 43.4 (2007): 415-430. <http://eudml.org/doc/33867>.

@article{Antoch2007,
abstract = {The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests for a detection of a change in an intensity of the Poisson process are described and illustrated by an example. We cover both the case when the time of the change is assumed to be known or unknown.},
author = {Antoch, Jaromír, Jarušková, Daniela},
journal = {Kybernetika},
keywords = {homogeneous and non-homogeneous Poisson process; counting process; change point detection; counting process; change point detection},
language = {eng},
number = {4},
pages = {415-430},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Testing a homogeneity of stochastic processes},
url = {http://eudml.org/doc/33867},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Antoch, Jaromír
AU - Jarušková, Daniela
TI - Testing a homogeneity of stochastic processes
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 415
EP - 430
AB - The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests for a detection of a change in an intensity of the Poisson process are described and illustrated by an example. We cover both the case when the time of the change is assumed to be known or unknown.
LA - eng
KW - homogeneous and non-homogeneous Poisson process; counting process; change point detection; counting process; change point detection
UR - http://eudml.org/doc/33867
ER -

References

top
  1. Antoch J., Hušková M., Estimators of changes, In: Nonparametrics, Asymptotics an Time Series (S. Ghosh, ed.), M. Dekker, New York 1998, pp. 533–578 (1998) MR1724708
  2. Antoch J., Hušková, M., Jarušková D., Off-line quality control, In: Multivariate Total Quality Control: Foundations and Recent Advances (N. C. Lauro et al. eds.), Springer–Verlag, Heidelberg 2002, pp. 1–86 MR1886415
  3. Barlow R. E., Proschan F., Mathematical Theory of Reliability, Wiley, New York 1964 Zbl0874.62111MR0195566
  4. Chernoff H., Zacks S., Estimating the current mean of normal distribution which is subjected to changes in time, Ann. Math. Statist. 35 (1964), 999–1018 (1964) MR0179874
  5. Cox D. R., Lewis P. A. W., The Statistical Analysis of Series of Events, Wiley, New York 1966 Zbl0195.19602MR0199942
  6. Csörgő M., Horváth L., Limit Theorems in Change Point Analysis, Wiley, New York 1997 MR2743035
  7. Embrechts P., Klüppelberg, C., Mikosch T., Modelling Extremal Events, Springer–Verlag, Heildelberg 1997 Zbl0873.62116MR1458613
  8. Haccou P., Meelis, E., Geer S. van de, The likelihood ratio test for the change point problem for exponentially distributed random variables, Stochastic Process. Appl. 27 (1988), 121–139 (1988) MR0934533
  9. Hájek J., Šidák Z., Theory of Rank Tests, Academia, Prague 1967 Zbl0944.62045MR0229351
  10. Kander Z., Zacks S., Test procedures for possible changes in parameters of statistical distributions occurring at unknown time points, Ann. Math. Statist. 37 (1966), 1196–1210 (1966) MR0202242
  11. Kiefer J., K-sample analogues of the Kolmogorov–Smirnov’s and Cramér–von Mises tests, Ann. Math. Statist. 30 (1960), 420–447 (1960) MR0102882
  12. Kotz S., Balakrishnan, M., Johnson N. L., Continuous Multivariate Distributions, Volume 1: Models and Applications. Wiley, New York 2000 Zbl0946.62001MR1788152
  13. Kvaløy J. T., Lindqvist B. H., TTT-based tests for trend in repairable systems data, Reliability Engineering and System Safety 60 (1998), 13–28 (1998) 
  14. Kvaløy J. T., Lindqvist B. H., Malmedal H., A statistical test for monotonic and non-monotonic trend in repairable systems, In: Proc. European Conference on Safety and Reliability – ESREL 2001, Torino 2002, pp. 1563–1570 
  15. Sigma, Natural Catastrophes and Major Losef in 1995, Sigma Publ. 2 (1995) (1995) 
  16. Steinebach. J., Eastwood V. R., On extreme value asymptotics for increments of renewal processes, J. Statist. Plann. Inference 44 (1995) (1995) Zbl0831.60060MR1342102
  17. Steinebach J., Eastwood V. R., Extreme value asymptotics for multivariate renewal processes, J. Multivariate Anal. 56 (1996), 284–302 (1996) Zbl0861.60065MR1379531

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.