Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials |
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| Authors: | S. Aki N. Balakrishnan S. G. Mohanty |
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| Affiliation: | (1) Department of Mathematical Science, Osaka University, 560 Toyonaka, Osaka, Japan;(2) Department of Mathematics and Statistics, McMaster University, L8S 4K1 Hamilton, Ontario, Canada |
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| Abstract: | 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.mconditional 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.This research was partially supported by the Natural Sciences and Engineering Research Council of Canada. |
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| Keywords: | Probability generating function diserete distributions sooner and later problem success and failure runs Markov chain waiting time |
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