Comparison of tests for bivariate normality with unknown parameters by transformation to an univariate statistic

Abstract

Fifteen tests for bivariate normality with unknown parameters have been compared. A Monte Carlo power analysis with componently independent uniform, lognormal and Student t4 distributions and with members of the family of bivariate gamma distributions as alternative hypothesis has been carried out. The Shapiro-Wilk- Stephens test has been found to perform well for all alternative distributions analyzed. The Shapiro-Wilk- Malkovich and Malkovich bl tests exhibit good power against the lognormal and the family of bivariate gamma distributions, but show poor power against independent uniform distributions. The bivariate test methods have been illustrated for the strength and elongation at break of Dyneema polyethylene yarn and nylon 6 monofilament. Dyneema is a trademark of DSM.