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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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