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 > >