On waiting time distributions associated with compound patterns in a sequence of multi-state trials |
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Authors: | Kiyoshi Inoue Sigeo Aki |
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Institution: | (1) Faculty of Economics, Seikei University, 3-3-1 Kichijoji-Kitamachi, Musasino-shi, Tokyo 180-8633, Japan;(2) Department of Mathematics, Faculty of Engineering, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan |
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Abstract: | In this article, waiting time distributions of compound patterns are considered in terms of the generating function of the
numbers of occurrences of the compound patterns. Formulae for the evaluation of the generating functions of waiting time are
given, which are very effective computational tools. We provide several viewpoints on waiting time problems associated with
compound patterns and develop a general workable framework for the study of the corresponding distributions. The general theory
is employed for the investigation of some examples in order to illustrate how the distributions of waiting time can be derived
through our theoretical results.
This research was partially supported by the ISM Cooperative Research Program (2006-ISM·CRP-2007). |
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Keywords: | Compound pattern Scan Run Multi-state trials Enumeration schemes Conditional distribution Probability function Probability generating function Double generating function |
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