Integrate the Multivariate normal distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg67451] Integrate the Multivariate normal distribution*From*: "Miguel Lejeune" <mlejeune at andrew.cmu.edu>*Date*: Sun, 25 Jun 2006 03:19:18 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I am using the MultiNormal function to compute the probability density function (pdf_ and cumulative probability distribution (cdf) of a bivraite normally distributed variable. I have two questions. 1) I followed the help file to get familiar with that function. But although I repeat what is indicated, I do not obtain the same output. Could you please indicate me? Example: In: Statistics`MultinormalDistribution In: (r = {{1, 0.2}, {0.2, 1}}; ndist = MultinormalDistribution[{0, 0}, r]) I obtain as output: Out: MultinormalDistribution [ {{0, 0}, {1, 0.2}, {1,0.2, 1}}] which is fine. However, when I type: In: pdf = PDF[ndist, {x1, x2}] The only output I obtain is: MultinormalDistribution[{0, 0}, {{1, 0.2}, {1, 0, 2}}] while in the help file it is indicated that I should obtain an algebraic expression. Why is it?? 2) My second question. I would like to proceed to the numerical integration of the CDF of the bivariate normal distribution. I enter: In: NIntegrate[CDF[ndist, {x1, x2}], {x1, -Infinity, 0}, {x2,-Infinity, 0}] I systematically obtain the following error message: "NIntegrate::inum: Integrand CDF[MultinormalDistribution[{0, 0}, {{1,0.5}, \ {1, 0, 5}}], {x1, x2}] is not numerical at {x1, x2} = {-1., -1.} " I do not understand why it is saying that the expression is not numerical at {-1,1}. Could anybody help? Many thanks, Miguel