Skip to main content Accessibility help
×
Home

On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials

  • James C. Fu (a1) and Y. M. Chang (a1)

Abstract

Probability generation functions of waiting time distributions of runs and patterns have been used successfully in various areas of statistics and applied probability. In this paper, we provide a simple way to obtain the probability generating functions for waiting time distributions of compound patterns by using the finite Markov chain imbedding method. We also study the characters of waiting time distributions for compound patterns. A computer algorithm based on Markov chain imbedding technique has been developed for automatically computing the distribution, probability generating function, and mean of waiting time for a compound pattern.

Copyright

Corresponding author

Postal address: Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada.
∗∗ Email address: james_fu@umanitoba.ca

Footnotes

Hide All

This work was supported in part by Nature Science and Engineering Research Council of Canada, under Grant A-9216.

Footnotes

References

Hide All
Aki, S., and Hirano, K. (1999). Sooner and later waiting time problems for runs in Markov dependent bivariate trials. Ann. Inst. Statist. Math. 51, 1729.
Balasubramanian, K., Viveros, R., and Balakrishnan, N. (1993). Sooner and later waiting time problems for Markovian Bernoulli trials. Statist. Prob. Lett. 18, 153161.
Boutsikas, M. V., and Koutras, M. V. (2000). Reliability approximation for Markov chain imbeddable systems. Methodol. Comput. Appl. Prob. 2, 393411.
Chao, M. T., and Fu, J. C. (1989). A limit theorem for certain repairable systems. Ann. Inst. Statist. Math. 41, 809818.
Chao, M. T., and Fu, J. C. (1991). The reliability of a large series system under Markov structure. Adv. Appl. Prob. 23, 894908.
Ebneshahrashoob, M., and Sobel, M. (1990). Sooner and later problems for Bernoulli trials: frequency and run quotas. Statist. Prob. Lett. 9, 511.
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn. John Wiley, New York.
Fu, J. C. (1986). Reliability of consecutive-k-out-of-n:F systems with (k-1)-step Markov dependence. IEEE Trans. Reliab. 35, 602606.
Fu, J. C. (1996). Distribution theory of runs and patterns associated with a sequence of multi-state trials. Statistica Sinica 6, 957974.
Fu, J. C., and Koutras, M. V. (1994). Distribution theory of runs: A Markov chain approach. J. Amer. Statist. Assoc. 89, 10501058.
Han, Q., and Aki, S. (1999). Joint distributions of runs in a sequence of multi-state trials. Ann. Inst. Statist. Math. 51, 419447.
Koutras, M. V. (1997). Waiting time distributions associated with runs of fixed length in two state Markov chains. Ann. Inst. Statist. Math. 49, 123139.
Koutras, M. V., and Alexandrou, V. A. (1997). Sooner waiting time problems in a sequence of trinary trials. J. Appl. Prob. 34, 593609.
Uchida, M. (1998). On generating functions of waiting time problems for sequence patterns of discrete random variables. Ann. Inst. Statist. Math. 50, 655671.

Keywords

MSC classification

On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials

  • James C. Fu (a1) and Y. M. Chang (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.