Abstract

This chapter discusses the tests of univariate and multivariate normality. The tests discussed in the chapter are tests based on descriptive measures, test based on cumulants, tests based on mean deviation, a test based on the range of the sample, omnibus tests based on moments, Shapiro–Wilk's W-test and its modifications, the modification of the W-test given by D'Agostino, , a shifted power transformation for assessing normality, a likelihood ratio test, goodness-of-fit tests, tests based on empirical distribution functions, and miscellaneous tests. The first formal test of multinormality has been proposed by Mardia through multivariate measures of skewness and kurtosis. The chapter discusses the strict multivariate procedures, radius and angles and graphical techniques, and nearest distance test. In the univariate case, Durbin has proposed a reduction of the composite null hypothesis of normality (versus non-normality) to a simple one using a randomized procedure. This technique is extended to the multivariate case by Wagle. As is usual with randomized procedures, a given set of data need not always yield the same decision.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.