Aki, S. (1992). Waiting time problems for a sequence of discrete random variables. Annals of the Institute of Statistical Mathematics
, 363–378.MathSciNetMATHCrossRefGoogle Scholar
Chang, Y. M. (2005). Distribution of waiting time until the \(r\)
th occurrence of acompound pattern. Statistics and Probability Letters
, 29–38.MathSciNetMATHCrossRefGoogle Scholar
Chang, Y. M., Wu, T. L. (2011). On average run lengths of control charts for autocorrelated processes. Methodology and Computing in Applied Probability, 13, 419–431.
Chang, Y. M., Fu, J. C., Lin, H. Y. (2012). Distribution and double generating function of number of patterns in a sequence of Markov dependent multistate trials. Annals of the Institute of Statistical Mathematics, 64, 55–68.
Cui, L., Xu, Y., Zhao, X. (2010). Developments and applications of the finite Markov chain imbedding approach in reliability. IEEE Transactions on Reliability, 59, 685–690.
Fu, J. C. (1996). Distribution theory of runs and patterns associated with a sequence of multi-state trials. Statistica Sinica
, 957–974.MathSciNetMATHGoogle Scholar
Fu, J. C., Koutras, M. V. (1994). Distribution theory of runs: a Markov chain approach. Journal of the American Statistical Association, 89, 1050–1058.
Fu, J. C., Lou, W. Y. W. (2003). Distribution theory of runs and patterns and its applications. River Edge, NJ: World Scientific Publishing Co. Inc.
Fu, J. C., Lou, W. Y. W., Wang, Y. J. (1999). On the exact distributions of Eulerian and Simon Newcomb numbers associated with random permutations. Statistics and Probability Letters, 42, 115–125.
Fu, J. C., Shmueli, G., Chang, Y. M. (2003). A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules. Statistics and Probability Letters, 65, 457–466.
Han, Q., Hirano, K. (2003). Sooner and later waiting time problems for patterns in Markov dependent trials. Journal of Applied Probability, 40, 73–86.
Hirano, K., Aki, S. (1993). On number of occurrences of success runs of specified length in a two-state Markov chain. Statistica Sinica, 3, 313–320.
Inoue, K., Aki, S. (2005). A generalized Pólya urn model and related multivariate distributions. Annals of the Institute of Statistical Mathematics, 57, 49–59.
Inoue, K., Aki, S. (2007). On generating functions of waiting times and numbers of occurrences of compound patterns in a sequence of multistate trials. Journal of Applied Probability, 44, 71–81.
Inoue, K., Aki, S. (2009). On waiting time distributions associated with compound patterns in a sequence of multi-state trials. Annals of the Institute of Statistical Mathematics, 61, 499–516.
Koutras, M. V. (1997). Waiting times and number of appearances of events in a sequence of discrete random variables (pp. 363–384). In Advances in combinatorial methods and applications to probability and statistics. Statistics for Industry and Technology. Boston, MA: Birkhäuser Boston
Koutras, M. V., Milienos, F. S. (2012). Exact and asymptotic results for pattern waiting times. Journal of Statistical Planning and Inference, 142, 1464–1479.
Lou, W. Y. W. (1996). On runs and longest run tests: a method of finite Markov chain imbedding. Journal of the American Statistical Association
, 1595–1601.MathSciNetMATHCrossRefGoogle Scholar
Nuel, G. (2008). Pattern Markov chains: Optimal Markov chain embedding through deterministic finite automata. Journal of Applied Probability
, 226–243.MathSciNetMATHCrossRefGoogle Scholar
Zhao, X., Cui, L. (2009). On the accelerated scan finite Markov chain imbedding approach. IEEE Transactions on Reliability, 58, 383–388.