Critical values and powers for tests of uniformity of directions under multivariate normality

Abstract

The Rayleigh, Ajne, Gin4 and two new tests of uniformity of directions are investigated as tests for multivariate normality when the population mean vector and covariance matrix are assumed to be unknown. The new tests include one which is designed especially to detect for bimodal alternatives and one which is designed to perform well under a wide variety of alternatives. Simulated percentile points are obtained under the assumption that the variates constitute a random sample from a multivariate normal distribution.Powers of the five tests are compared under alternatives in the bivariate as well as higher dimensional settings.

An Appraisal and Bibliography of Tests for Multivariate Normality

“…Uniformity of the angles indicates normality of the multivariate data. Dunn (1995) suggested that Koziol's 'radii and angles' test could be improved by replacing the Rayleigh test statistic for uniformity with a more powerful substitute. Tsai & Koziol (1988) presented a procedure that utilized the correlation coefficient of the chi-square plot.…”