mardia {mvnormalTest}

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)

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.

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).

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)