# AD.test: Anderson-Darling test for multivariate normality In mvnTest: Goodness of Fit Tests for Multivariate Normality

## Description

This function implements the Anderson-Darling test for assessing multivariate normality. It calculates the value of the test and its approximate p-value.

## Usage

 `1` ``` AD.test(data, qqplot = FALSE) ```

## Arguments

 `data` A numeric matrix or data frame. `qqplot` If `TRUE` produces a chi-squared QQ plot.

## Value

 `AD` the value of the test statistic. `p.value` the p-value of the test.

## 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

Paulson, A., Roohan, P., and Sullo, P. (1987). Some empirical distribution function tests for multivariate normality. Journal of Statistical Computation and Simulation, 28, 15-30

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

Selcuk Korkmaz, Dincer Goksuluk, and Gokmen Zararsiz. MVN: Multivariate Normality Tests, 2015. R package version 4.0

`S2.test`, `CM.test`, `DH.test`, `R.test`, `HZ.test`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## 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 <- AD.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 <- AD.test(dat) res1 data(iris) setosa <- iris[1:50, 1:4] # Iris data only for setosa res2 <- AD.test(setosa, qqplot = TRUE) res2 ## End(Not run) ```