2003 Fiscal Year Final Research Report Summary
A multivariate extension of inverse Gaussian distribution: theory and applications
| Project/Area Number |
14580355
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
MINAMI Mihoko The Institute of Statistical Mathematics, Department of Fundamental Statistical Theory, Associate Professor, 統計基礎研究系, 助教授 (70277268)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Multivariate inverse Gaussian distribution / inverse relationship / Brownian motion / Multivariate Lagrange distribution / first hitting time / waiting time distribution / Multivariate normal distribution |
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| Research Abstract |
We proposed a new multivariate extension of the inverse Gaussian distribution derived from multivariate inverse relationship. First we define the inverse relationship between two sets of multivariate distributions and the reduced inverse relationship between two multivariate distributions. Them, we derive the multivariate continuous distribution that has the reduced multivariate inverse relationship with a multivariate normal distribution and call it a multivariate inverse Gaussian distribution. This distribution is also characterized as the distribution of the location of a multivariate Brownian motion at some stopping time. The marginal distribution in one direction is the inverse Gaussian distribution and the conditional distribution in the space perpendicular to this direction is a multivariate normal distribution. Mean variance and higher order cumulants are derived from the multivariate inverse relationship with a multivariate normal distribution Other properties such as reproductivity and maximum likelihood estimates are also given. These results were published as a paper.
The multivariate inverse relationship is also satisfied among multivariate Lagrange distributions and their arriving distributions. It can be shown that under some conditions, multivariate Lagrange distributions converge to multivariate inverse Gaussian distributions that we proposed. A paper that discusses these results is in preparation.
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Research Products
(2 results)
