Distribution theory of runs and patterns associated with a sequence of multi-state trials

Statistica Sinica

Volumn 6, Issue 4, 1996, Pages 957-974

  Fu, James C ^a  

^a NATIONAL DONG HWA UNIVERSITY   (Taiwan)

Author keywords

Distributions of runs and patterns; Markov chain; Multi state trials; Transition probability matrix

Indexed keywords

EID: 21444442040     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Balasubramanian, K., Viveros, R. and Balakrishnan, N. (1993). Sooner and later waiting time problems for Markovian Bernoulli trials. Statist. Probab. Lett. 18, 153-161.
2. Benevento, R. V. (1984). The occurrence of sequence patterns in ergodic Markov chains. Stochastic Process. Appl. 17, 369-373.
3. Chao, M. T. and Fu, J. C. (1989). A limit theorem of certain repairable systems. Ann. Inst. Statist. Math. 41, 809-818.
4. Chao, M. T. and Fu, J. C. (1991). The reliability of large series systems under Markov structure. Adv. Appl. Probability 23, 894-908.
5. Cochran, W. G. (1938). An extension of Gold's method for examining the apparent persistence of one type of weather. Roy. Meteorol. Soc. Quart. Journal 64, 631-634.
6. Ebneshahrashoob, M. and Sobel, M. (1990). Sooner and later waiting time problems for Bernoulli trials : frequency and run quotas. Statist. Probab. Lett. 9, 5-11.
7. Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol.I, 3rd ed., John Wiley, New York.
8. Fu, J. C. (1986). Reliability of consecutive-k-out-of-n : F systems with (k - 1)-step Markov dependence. IEEE Trans. Reliability R35, 602-606.
9. Fu, J. C. (1995). Exact and limiting distributions of the number of successions in a random permutation. Ann. Inst. Statist. Math. 47, 435-446.
10. Fu, J. C. and Koutras, M. V. (1994). Distribution theory of runs : A Markov chain approach. J. Amer. Statist. Assoc. 89, 1050-1058.
11. Gibbons, J. D. (1985). Non-parametric Statistical Inference. M. Dekker, New York.
12. Hahn, G. J. and Gage, J. B. (1983). Evaluation of a start-up demonstration test. J. Qual. Technol. 15, 103-106.
13. Koutras, M. V. and Papastavridis, S. G. (1993). On the number of runs and related statistics. Statist. Sinica 3, 277-294.
14. Mood, A. M. (1940). The distribution theory of runs. Ann. Math. Statist. 11, 367-392.
15. Mosteller, F. (1941). Note on an application of runs to quality control charts, Ann. Math. Statist. 12, 228-232.
16. Schwager, S. J. (1983). Run probabilities in sequences of Markov-dependent trials. J. Amer. Statist. Assoc. 78, 168-175.
17. Stevens, W. L. (1939). Distributions of groups in a sequence of alternatives. Ann. of Eugenics 9, 10-17.
18. Wald, A. and Wolfowitz, J. (1940). On a test whether two samples are from the same population. Ann. Math. Statist. 11, 147-162.
19. Walsh, J. E. (1965). Handbook of Non-Parametric Statistics. D. Van Nostrand Company, Inc. New York.
20. Wishart, J. and Hirshfeld, H. O. (1936). A theorem concerning the distribution of joins between line segments. London Math. Soc. J. 11, 227-235.
21. Wolfowitz, J. (1943). On the theory of runs with some applications to quality control, Ann. Math. Statist. 14, 280-288.