CORRELATED MULTIVARIATE SHOCK MODELS ASSOCIATED WITH A RENEWAL SEQUENCE AND ITS APPLICATION TO ANALYSIS OF BROWSING BEHAVIOR OF INTERNET USERS
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- Sumita Ushio
- University of Tsukuba
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- Zuo Jinshui
- University of Tsukuba
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Abstract
A correlated multivariate shock model is considered where a system is subject to a sequence of J different shocks triggered by a common renewal process. Let (Y(k))^∞_<k=1> be a sequence of independently and identically distributed (i.i.d.) nonnegative random variables associated with the renewal process. For the magnitudes of the k-th shock denoted by a random vector X__-(k), it is assumed that [X__-(k),Y(k)] (k=1,2,…) constitute a sequence of i.i.d. random vectors with respect to k while X__-(k) and Y(k) may be correlated. The system fails as soon as the historical maximum of the magnitudes of any component of the random vector exceeds a prespecified level of that component. The Laplace transform of the probability density function of the system lifetime is derived, and its mean and variance are obtained explicitly. Furthermore, the probability of system failure due to the i-th component is obtained explicitly for all i∈J={1,…,J}. The model is applied for analyzing the browsing behavior of Internet users.
Journal
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- Journal of the Operations Research Society of Japan
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Journal of the Operations Research Society of Japan 53 (2), 119-135, 2010
The Operations Research Society of Japan
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Details 詳細情報について
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- CRID
- 1390001204110881536
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- NII Article ID
- 110007641867
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- NII Book ID
- AA00703935
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- ISSN
- 21888299
- 04534514
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- NDL BIB ID
- 10711680
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed