Cramer-von Mises test for Multivariate Normality

Description

This function implements the Cramer-von Mises test for assessing multivariate normality.

Usage

1

Arguments

data

A numeric matrix or data frame

qqplot

if TRUE creates a chi-square Q-Q plot

Details

Calculates the value of the Cramer-von Mises test and the approximate p-value.

Value

CM

the value of the test statistic

p.value

the p-value of the test

data.name

a character string giving the name of the data

Note

The printing method and plotting are in part adapted from R package MVN (version 4.0, Korkmaz, S. et al., 2015).

The computations are relatively expensive as Monte Carlo procedure is used to calculate empirical p-vales.

Author(s)

Rashid Makarov, Vassilly Voinov, Natalya Pya

References

Koziol, J. (1982). A class of invariant procedures for assessing multivariate normality. Biometrika, 69, 423-427

Henze, N. and Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in Statistics - Theory and Methods, 19, 3595-3617

See Also

S2.test, AD.test, DH.test, R.test, HZ.test

Examples

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## Not run: 
## generating n bivariate normal random variables...       
dat <- rmvnorm(n=100,mean=rep(0,2),sigma=matrix(c(4,2,2,4),2,2)) 
res <- CM.test(dat)
res

## generating n bivariate t distributed with 10df random variables...       
dat <- rmvt(n=200,sigma=matrix(c(4,2,2,4),2,2),df=10,delta=rep(0,2)) 
res1 <- CM.test(dat)
res1

data(iris)
setosa <- iris[1:50, 1:4] # Iris data only for setosa
res2 <- CM.test(setosa, qqplot = TRUE)
res2

## End(Not run)