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Sooner and Later Waiting Time Problems for Runs in Markov Dependent Bivariate Trials |
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| Authors: | Sigeo Aki Katuomi Hirano |
| Institution: | (1) Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, 560-8531, Japan;(2) The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan |
| Abstract: | In this paper we study exact distributions of sooner and later waiting times for runs in Markov dependent bivariate trials. We give systems of linear equations with respect to conditional probability generating functions of the waiting times. By considering bivariate trials, we can treat very general and practical waiting time problems for runs of two events which are not necessarily mutually exclusive. Numerical examples are also given in order to illustrate the feasibility of our results. |
| Keywords: | Discrete distributions probability generating function run waiting time problem |
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