Re: Integrate the Multivariate normal distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg67456] Re: [mg67451] Integrate the Multivariate normal distribution
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 26 Jun 2006 00:12:57 -0400 (EDT)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
You need to load the package.
Off[General::spell1];
Needs["Statistics`MultinormalDistribution`"];
r={{1,0.2},{0.2,1}};
ndist=MultinormalDistribution[{0,0},r];
pdf=PDF[ndist,{x1,x2}]
0.16243683359034922*
E^((1/2)*((-x1)*(1.0416666666666667*x1 -
0.20833333333333337*x2) -
x2*(1.0416666666666667*x2 - 0.20833333333333337*x1)))
ContourPlot[pdf,{x1,-2,2},{x2,-2,2}];
NIntegrate[CDF[ndist,{x1,x2}],
{x1,-Infinity,0},{x2,-Infinity,0}]
0.212349
Bob Hanlon
---- Miguel Lejeune <mlejeune at andrew.cmu.edu> wrote:
> 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
>
>