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Biometrika 1975 62(2):393-396; doi:10.1093/biomet/62.2.393
© 1975 by Biometrika Trust
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Integrals for one-sided confidence bounds: A general result

H. P. WYNN

Department of Mathematics, Imperial College London

Certain multivariate normal and t integrals have bean calculated by Bohrer and Francis and others to find confidence bounds in regression analysis. Their technique of partitioning Rn into disjoint regions is generalized to bounds based on arbitrary polyhedral cones. A geometrical solution for cones in R3 results. The probabilities are also those arising from tests for a multivariate mean against alternatives lying in such cones, developed by Bratholomew and others.

Key Words: Geometrical probability • Multivariate normal distribution • Multivariate t distribution • Simultaneous confidence bands


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