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Estimation of $$\Pr (a'x>b'y)$$ in the multivariate normal case. (English) Zbl 0699.62053
Summary: We consider two non-independent random vectors $$x_{p\times 1}$$ and $$y_{q\times 1}$$ having multivariate normal distribution and obtain the maximum likelihood and the minimum variance unbiased estimates of $$R=\Pr (a'x>b'y)$$ where a and b are two known vectors.
The problem arises, for example, in a system where the energy is supplied to the system by p sources and is consumed through q sources. Some interesting special cases are deduced. A simulation study was carried out to compare the MVUE and MLE of R. An application is provided to determine the effect of a certain drug on the level of biochemical compounds found in the brain.

##### MSC:
 62H12 Estimation in multivariate analysis 62P10 Applications of statistics to biology and medical sciences; meta analysis
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##### References:
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