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