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One tailed tests of means for multivariate normal distributions derived by generalized geometric programming. (English) Zbl 1264.90140

Summary: This paper studies multivariate one-tailed tests of the means, which occur in many application areas of statistics. The statistical distribution of the single-sided statistic is found using the union-intersection principle of S. N. Roy to formulate the estimation problem and generalized geometric programming to analyze and solve it. Generalized geometric programming is the key to the solution as it converts the primal problem into a dual problem, which is effectively zero degree of difficulty and thus relatively easy to solve. The generalized \(t\)-statistic \((GT)\) is developed. \((GT)^2\) is a generalization of the Hotelling \(T^2\) statistic. This is based on a generalized \(F\) statistic, which can be found by solving an equation. Statistical tables are provided. The statistic is used to perform an hypothesis test in senility using the Wechsler Adult Intelligent Scale.

MSC:

90C25 Convex programming
90C32 Fractional programming
97K80 Applied statistics (educational aspects)
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