Moments of the multivariate normal distribution

[Chris]

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
cj...@umich.edu

[ipar...@cajamadrid.es]

Hi,

I strongly suggest that you buy the following book:

Mathematical Statistics with Mathematica

Authors

Colin Rose

Murray D. Smith

there you'll find the answer you looking for and more.

cheers

yannis

-----Mensaje original-----
De: cj...@umich.edu [mailto:cj...@umich.edu]
Enviado el: martes 21 de enero de 2003 13:40
Para: math...@smc.vnet.net
Asunto: Moments of the multivariate normal distribution