caa a22 4500 477063004 CHVBK 20180405111406.0 cr unu---uuuuu 170330e19961201xx s 000 0 eng 10.1007/BF00052332 doi (NATIONALLICENCE)springer-10.1007/BF00052332 Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials [Elektronische Daten] [S. Aki, N. Balakrishnan, S. Mohanty] The probability generating functions of the waiting times for the first success run of length k and for the sooner run and the later run between a success run of length k and a failure run of length r in the second order Markov dependent trials are derived using the probability generating function method and the combinatorial method. Further, the systems of equations of 2.m conditional probability generating functions of the waiting times in the m-th order Markov dependent trials are given. Since the systems of equations are linear with respect to the conditional probability generating functions, they can be solved exactly, and hence the probability generating functions of the waiting time distributions are obtained. If m is large, some computer algebra systems are available to solve the linear systems of equations. The Institute of Statistical Mathematics, 1996 Probability generating function nationallicence diserete distributions nationallicence sooner and later problem nationallicence success and failure runs nationallicence Markov chain nationallicence waiting time nationallicence Aki S. Department of Mathematical Science, Osaka University, 560, Toyonaka, Osaka, Japan aut Balakrishnan N. Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada aut Mohanty S. Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 773-787 0020-3157 48:4<773 1996 48 10463 https://doi.org/10.1007/BF00052332 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00052332 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aki S. Department of Mathematical Science, Osaka University, 560, Toyonaka, Osaka, Japan aut NATIONALLICENCE 700 1- Balakrishnan N. Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada aut NATIONALLICENCE 700 1- Mohanty S. Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/4(1996-12-01), 773-787 0020-3157 48:4<773 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer