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RE: Moments of the multivariate normal distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38940] RE: [mg38958] Moments of the multivariate normal distribution
  • From: iparaske at cajamadrid.es
  • Date: Wed, 22 Jan 2003 06:09:36 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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: cjque at umich.edu [mailto:cjque at umich.edu]
Enviado el: martes 21 de enero de 2003 13:40
Para: mathgroup at smc.vnet.net
Asunto: [mg38958] Moments of the multivariate normal distribution


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



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