mvnormalTest (version 1.0.1)

mardia: Mardia Test (Skewness and Kurtosis) for Multivariate Normality

Description

It computes Mardia (1970)'s multivariate skewness and kurtosis statistics and their corresponding p-value. Both p-values of skewness and kurtosis statistics should be greater than 0.05 to conclude multivariate normality. The skewness statistic will be adjusted for sample size \(n < 20\).

Usage

mardia(X, std = TRUE)

Value

Returns a list with two objects:

mv.test

results of the Mardia test, i.e., test statistic, p-value, and multivariate normality summary (YES, if both skewness and kurtosis p-value>0.05).

uv.shapiro

a dataframe with \(p\) rows detailing univariate Shapiro-Wilk tests. Columns in the dataframe contain test statistics W, p-value,and univariate normality summary (YES, if p-value>0.05).

Arguments

X

an \(n*p\) numeric matrix or data frame.

std

if TRUE, the data matrix or data frame will be standardized via normalizing the covariance matrix by \(n\).

References

Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530.

Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3/4), 591-611.

Doornik, J. A., & Hansen, H. (2008). An omnibus test for univariate and multivariate normality. Oxford Bulletin of Economics and Statistics, 70, 927-939.

Zhou, M., & Shao, Y. (2014). A powerful test for multivariate normality. Journal of applied statistics, 41(2), 351-363.

See Also

mvnTest, faTest, msw, msk, mhz, mvn

Examples

set.seed(12345)

## Data from gamma distribution
X = matrix(rgamma(50*4,shape =  2),50)
mardia(X)

## Data from normal distribution
X = matrix(rnorm(50*4,mean = 2 , sd = 1),50)
mardia(X)

## load the ubiquitous multivariate iris data ##
## (first 50 observations of columns 1:4) ##
iris.df = iris[1:50, 1:4]
mardia(iris.df)