Moments of the multivariate normal distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg38958] Moments of the multivariate normal distribution
- From: cjque at umich.edu (Chris)
- Date: Tue, 21 Jan 2003 07:40:12 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello,
I am trying to use mathematica to define moment generating function of
a multivariate normal distribution with mean 0 and variance T,
[N(0,T)]. I would like to be able to find the nth moment for this
distribution.
For simplicity I would like define m = exp[1/2 b'T b]= f(b), where b
is a q*1 vector with elements (b1 b2 b3 b4 ... bq) (b' is 1*q), and T
is a q*q matrix with elements
t11 t12 t13 ... t1q
t21 t22 t23 ... t2q
. . . .
. . . .
. . . .
tq1 tq2 tq3 tqq
I have looked through the online manual and have only found out how to
define a matrix or vector of specific integer size.
I have found the first moment which disapears at b=0 to be
m*b'*T.
I have also found the second moment to be
m*T + m*T*b*b'T.
I am having a very hard problem finding the next moment (let alone the
next ten). I would like to use mathematica to get all the momnets I
care to look at. I would be greatful for any help!!
Thanks a Lot,
Chris Johnson
cjque at umich.edu