Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials

Annals of the Institute of Statistical Mathematics

Volumn 48, Issue 4, 1996, Pages 773-787

  Aki, S ^a   Balakrlshnan, N ^b   Mohanty, S G ^b  

^a OSAKA UNIVERSITY   (Japan)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

Discrete distributions; Markov chain; Probability generating function; Sooner and later problem; Success and failure runs; Waiting time

Indexed keywords

EID: 0001120244     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00052332     Document Type: Article

References (27)

1. Aki, S. (1992). Waiting time problems for a sequence of discrete random variables, Ann. Inst. Statist. Math., 44, 363-378.
2. Aki, S. and Hirano, K. (1993). Discrete distributions related to succession events in a two-state Markov chain, Statistical Science & Data Analysis (eds. K. Matusita, M. L. Puri and T. Hayakawa), 467-474, VSP Publishers, Amsterdam.
3. Balasubramanian, K., Viveros, R. and Balakrishnan, N. (1993). Sooner and later waiting time problem for Markovian Bernoulli trials, Statist. Probab. Lett., 18, 153-161.
4. Crysaphinou, O. and Papastavridis, S. (1990). The occurrence of sequence patterns in repeated dependent experiments, Theory Probab. Appl., 35, 145-152.
5. Crysaphinou, O., Papastavridis, S. and Tsapelas, T. (1994). On the waiting time appearance of given patterns, Runs and Patterns in Probability: Selected Papers (eds. A. P. Godbole and S. G. Papastavridis), 231-241, Kluwer, Dordrecht.
6. Derman, C., Lieberman, G. J. and Ross, S. M. (1982). On the consecutive-k-of-n:F system, IEEE Transactions on Reliability, R-31, 57-63.
7. Ebneshahrashoob, M. and Sobel, M. (1990). Sooner and later problems for Bernoulli trials: frequency and run quotas, Statist. Probab. Lett., 9, 5-11.
8. Fu, J. C. (1986). Reliability of consecutive-k-out-of-n:F systems with (k-1)-step Marcov dependence, IEEE Transactions on Reliability, R-35, 602-606.
9. Fu, J. C. and Koutras, M. V. (1994). Distribution theory of runs: A Markov chain approach, J. Amer. Statist. Assoc., 89, 1050-1058.
10. Godbole, A. P. (1993). Approximate reliabilities of m-consecutive-k-out-of-n:failure systems, Statistica Sinica, 3, 321-327.
11. Godbole, A. P. and Papastavridis, S. G. (1994). Runs and Patterns in Probability: Selected Papers, Kluwer, Dordrecht.
12. Hahn, G. J. and Gage, J. B. (1983). Evaluation of a start-up demonstration test, Journal of Quality Technology, 15, 103-106.
13. Hirano, K. (1986). Some properties of the distributions of order k, Fibonacci Numbers and Their Applications (eds. A. N. Philippou, G. E. Bergum and A. F. Horadam), 43-53, Reidel, Dordrecht.
14. Hirano, K. and Aki, S. (1993). On number of occurrences of success runs of specified length in a two-state Markov chain, Statistica Sinica, 3, 313-320.
15. Johnson, N. L., Kotz, S. and Kemp, A. W. (1992). Univariate Discrete Distributions, Wiley, New York.
16. Lambiris, M. and Papastavridis, S. G. (1987). Reliability of a consecutive-k-out-of-n:F system for Markov dependent components, IEEE Transactions on Reliability, R-36, 78-79.
17. Mohanty, S. G. (1994). Success runs of length k in Markov dependent trials, Ann. Inst. Statist. Math., 46, 777-796.
18. Papastavridis, S. and Lambiris, M. (1987). Reliability of a consecutive-k-out-of-n:F system for Markov-dependent components, IEEE Transactions on Reliability, R-36, 78-79.
19. Philippou, A. N. (1986). Distributions and Fibonacci polynomials of order k, longest runs, and reliability of consecutive-k-out-of-n:F system, Fibonacci Numbers and Their Applications (eds. A. N. Philippou, G. E. Bergum and A. F. Horadam), 203-227, Reidel, Dordrecht.
20. Philippou, A. N. and Makri, F. S. (1986). Successes, runs, and longest runs, Statist. Probab. Lett., 4, 101 105.
21. Philippou, A. N. and Muwafi, A. A. (1982). Waiting for the k-th consecutive success and the Fibonacci sequence of order k, Fibonacci Quart., 20, 28-32.
22. Philippou, A. N., Georghiou, C. and Philippou, G. N. (1983). A generalized geometric distribution and some of its properties, Statist. Probab. Lett., 1, 171-175.
23. Rajarshi, M. B. (1974). Success runs in a two-state Markov chain, J. Appl. Probab., 11, 190-192.
24. Schwager, S. J. (1983). Run probability in sequences of Markov-dependent trials, J. Amer. Statist. Assoc., 78, 168-175.
25. Stanley, R. T. (1986). Enumerative Combinatorics, Wadsworth Publishers, Kentucky.
26. Viveros, R. and Balakrishnan, N. (1993). Statistical inference from start-up demonstration test data, Journal of Quality Technology, 25, 119-130.
27. Viveros, R., Balasubramanian, K. and Balakrishnan, N. (1994). Binomial and negative binomial analogues under correlated Bernoulli trials, Amer. Statist., 48, 243-247.