caa a22 4500 475826833 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1017537629251 doi (NATIONALLICENCE)springer-10.1023/A:1017537629251 Waiting Time Problems in a Two-State Markov Chain [Elektronische Daten] [Qing Han, Sigeo Aki] Let F 0 be the event that l 0 0-runs of length k 0 occur and F 1 be the event that l 1 1-runs of length k 1 occur in a two-state Markov chain. In this paper using a combinatorial method and the Markov chain imbedding method, we obtained explicit formulas of the probability generating functions of the sooner and later waiting time between F 0 and F 1 by the non-overlapping, overlapping and "greater than or equal" enumeration scheme. These formulas are convenient for evaluating the distributions of the sooner and later waiting time problems. The Institute of Statistical Mathematics, 2000 Waiting time problems nationallicence discrete distributions of order k nationallicence Markov chain nationallicence Markov chain imbedding method nationallicence probability generating function nationallicence Han Qing Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, 560-8531, Osaka, Japan aut Aki Sigeo Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, 560-8531, Osaka, Japan aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 778-789 0020-3157 52:4<778 2000 52 10463 https://doi.org/10.1023/A:1017537629251 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1017537629251 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Han Qing Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, 560-8531, Osaka, Japan aut NATIONALLICENCE 700 1- Aki Sigeo Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, 560-8531, Osaka, Japan aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 778-789 0020-3157 52:4<778 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer