# multivariate normal

1. ### Conditional Multi-variate Normal Distribution

Dear all, I would like to find a computationally quick and sufficiently accurate way (i.e., either analytically or numerical approximation) to compute a conditional probability for a specific multi-variate normal distribution, which is defined as follows: Let x1, ..., xn be n normal I.I.D...
2. ### Multivariate normal distribution, not full rank, probability density function

If X has a multivariate distribution of full rank and Y is the sum of the elements of X. Then (X,Y) is a multivariate normal distribution but not of full rank, then as I understand you can not calculate a density function for it. However would I be able to say the density function of (X,Y) is...
3. ### Multivariate Normality accepted at 5% significance level but rejected at 1% ??

Hi, I am new to this forum. I am trying to test whether a set of variables in the data follow multivariate normal distribution. I found Mardia's test for this and below is the summary of the results : Mardia Skewness 58.29 <.0001 Mardia Kurtosis 2.43 0.0149 Henze-Zirkler T 7.52 <.0001...
4. ### The multi-factor model is a multivariate gaussian distribution?

I'm sure that the following question is trivial, but I can't found a solid demonstration. Can we state that multi-factor model is a multivariate gaussian distribution? multi-factor model: X_ij = sigma_i * Z_i + sqrt(1-sigma_i^2)* E_ij where i=1,...,k j=1,...,n_i 0 < sigma_i <...
5. ### characterization of multivariate normal distribution by covariances

Hi, the professor told us that a multivariate normal distribution can be characterized as the only distribution for which zero covariance implies independence. How can you prove this? Can you give me a reference for this proof? Thank you