# mhz: Henze-Zirkler Test for Multivariate Normality In mvnormalTest: Powerful Tests for Multivariate Normality

## Description

It computes a multiviariate normality test based on a non-negative functional distance which was proposed by Henze and Zirkler (1990). Under the null hypothesis the test statistic is approximately log-normally distributed.

## Usage

 `1` ```mhz(X) ```

## Arguments

 `X` an n*p numeric matrix or data frame.

## Value

Returns a list with two objects:

`mv.test`

results of the Henze-Zirkler test, i.e., test statistic, p-value, and multivariate normality summary (YES, if 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

Henze, N., & Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in statistics-Theory and Methods, 19(10), 3595-3617.

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

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

`power.mhz`, `mvnTest`, `faTest`, `msw`, `msk`, `mardia`, `mvn`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```set.seed(12345) ## Data from gamma distribution X = matrix(rgamma(50*4,shape = 2),50) mhz(X) ## Data from normal distribution X = matrix(rnorm(50*4,mean = 2 , sd = 1),50) mhz(X) ## load the ubiquitous multivariate iris data ## ## (first 50 observations of columns 1:4) ## iris.df = iris[1:50, 1:4] mhz(iris.df) ```

### Example output

```\$mv.test
Statistic   p-value    Result
1.194     5e-04        NO

\$uv.shapiro
W      p-value UV.Normality
V1 0.9226 0.0029  No
V2 0.9056 7e-04   No
V3 0.9106 0.0011  No
V4 0.959  0.0808  Yes

\$mv.test
Statistic   p-value    Result
0.7224    0.6299       YES

\$uv.shapiro
W      p-value UV.Normality
V1 0.9812 0.6023  Yes
V2 0.9552 0.0561  Yes
V3 0.9799 0.5489  Yes
V4 0.9847 0.7595  Yes

\$mv.test
Statistic   p-value    Result
0.9488      0.05        NO

\$uv.shapiro
W      p-value UV.Normality
Sepal.Length 0.9777 0.4595  Yes
Sepal.Width  0.9717 0.2715  Yes
Petal.Length 0.955  0.0548  Yes
Petal.Width  0.7998 0       No
```

mvnormalTest documentation built on April 28, 2020, 5:06 p.m.