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Re: Integrate the Multivariate normal distribution
*To*: mathgroup at smc.vnet.net
*Subject*: [mg67466] Re: [mg67451] Integrate the Multivariate normal distribution
*From*: "Miguel Lejeune" <mlejeune at andrew.cmu.edu>
*Date*: Mon, 26 Jun 2006 00:54:17 -0400 (EDT)
*References*: <31541561.1151237675216.JavaMail.root@eastrmwml07.mgt.cox.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Thank you Bob.
I have one more question, also related to the bivariate normal distribution.
I would like to compute (numerically) the following integrale (PDF is the
probability density function of the bivariate normal distribution):
Integrale of [PDF[ndist, {x1, x2}] with respect to x2 (dx2) and the
integration bounds are -Infinity and 1.
with
ndist = MultinormalDistribution[{0, 0}, r];
r = {{1, 0.2}, {0.2, 1}};
Could you indicate me how I should do?
Many thanks,
Miguel
----- Original Message -----
From: "Bob Hanlon" <hanlonr at cox.net>
To: mathgroup at smc.vnet.net
Subject: [mg67466] Re: [mg67451] Integrate the Multivariate normal distribution
> 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
>>
>>
>
>
>
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