joint normal distribution
are normal (http://planetmath.org/NormalRandomVariable). This implies, in particular, that the individual random variables are each normally distributed. However, the converse is not not true and sets of normally distributed random variables need not, in general, be jointly normal.
Then, the joint normal distribution is commonly denoted as . Conversely, this distribution exists for any such and .
The joint normal distribution has the following properties:
If has the distribution and then
Sets of linear combinations of joint normals are themselves joint normal. In particular, if and is an matrix, then has the joint normal distribution .
The characteristic function is given by
for and any .
|Title||joint normal distribution|
|Date of creation||2013-03-22 15:22:34|
|Last modified on||2013-03-22 15:22:34|
|Last modified by||gel (22282)|
|Synonym||multivariate Gaussian distribution|
|Defines||multivariate normal distribution|