# Multivariate Normal Distribution

We extend the univariate normal distribution (as described in Normal Distribution) to the multivariate domain.

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### 11 Responses to Multivariate Normal Distribution

1. Tamas Banyasz says:

Charles,
Thank you for your work. It is a great help in my research work.
You have the talent to build a bridge between professional statistician and common users.
Have you ever considered publishing your work in a printed book? I would be happy to see that on my shelf.

Tom

• Charles says:

Tamas,
Thank you for your kind remarks. I try my best to make statistics accessible to everyone.
I am planning to release an ebook shortly.
Charles

• Romil says:

Charles,

Can you show us how to solve A generalization of Shapiro-Wilk for Multivariate Normality.. I recently conducting this study for my undergraduate thesis. my adviser wants me to solve this manually using excel. hope you can help me this one.

Thank you.

• Charles says:

Romil,

I haven’t implemented a test for multivariate normality yet.

In any case, here is a paper that describes the state of the art today.

https://www.stat.ubc.ca/~matias/mvn-scs5.pdf

I was planning on implementing the the approaches described in references [10] and [19].

Charles

2. Lola says:

If I am running bivariate parametric tests do both the interpendent and dependent variable need to be normally distributed or just the dependent variable?

• Charles says:

Lola,
Which test are you running?
Charles

• Lola says:

Chi-square, Kruskals Tau.

Possibly t-test/anova

Correlations

• Charles says:

Lola,
For these types of tests, you are checking the normality of the dependent variables. The independent variables are categorical (and so won’t be normal). I suggest that you look at the assumptions for each test separately.
Charles

3. Estimado Dr. excuseme, si la matriz de datos no tienen distribución normal multivariante, podemos utilizar la caja de Cox Transformación?
Y si esta transformación no tienen distribución normal multivariante, ¿cómo podría ser el trabajo con estos datos ?.
Dear Dr. excuseme, if data matrix do not have Multivariate Distribution Normal, we can use Box Cox Transformation?
And if this transformation do not have Multivariate Distribution Normal, how could be work with this data?.

• Charles says:

Gerardo,
The Box-Cox transformation can be used to transform one sample at a time (univariate normality). This doesn’t guarantee that the combined sample will be multivariate normal, but it might be. See Box-Cox Transformation.
You can use Mardia’s test to check for multivariate normality. See the webèpage http://www.real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-testing/
Most multivariate tests are quite robust for violations of multivariate normality, and so it is likely that the test will work even if the data is not multivariate normal. I would think that if univariate normality is achieved you are probably ok (although there is no guarantee).
Charles

• Thank you, Sir