Re: MultinormalDistribution Question
- To: mathgroup at smc.vnet.net
- Subject: [mg120177] Re: MultinormalDistribution Question
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 11 Jul 2011 06:58:36 -0400 (EDT)
- Reply-to: hanlonr at cox.net
Clear[x, y]; mean1 = 58/10; sigma1 = 2/10; mean2 = 53/10; sigma2 = 2/10; rho = 6/10; dist = MultinormalDistribution[{mean1, mean2}, {{sigma1^2, rho*sigma1*sigma2}, {rho*sigma1*sigma2, sigma2^2}}]; plot1 = Plot3D[PDF[dist, {x, y}], {x, mean1 - 3 sigma1, mean1 + 3 sigma1}, {y, mean2 - 3 sigma2, mean2 + 3 sigma2}, PlotRange -> All] m = Integrate[y*PDF[dist, {63/10, y}], {y, -Infinity, Infinity}] (14*Sqrt[2/Pi])/E^(25/8) m // N 0.490792 Alternatively, m == Expectation[y*DiracDelta[x - 63/10], Distributed[{x, y}, dist]] True s = Sqrt[Integrate[(y - m)^2*PDF[dist, {63/10, y}], {y, -Infinity, Infinity}]]; s // N 1.51329 Alternatively, s == N[Sqrt[Expectation[(y - m)^2*DiracDelta[x - 63/10], Distributed[{x, y}, dist]]]] True Bob Hanlon ---- Steve <s123 at epix.net> wrote: ============= Hello, Can someone help me with this ? I have 2 normal distributions; dist1 describes x and dist2 describes y. Each are fully defined and are correlated to one another by the correlation coefficient. How can I detemine the mean and standard deviation of the expected normal distribution that is associated with a given x value from dist1 ? An example: mean1 = 5.8 sigma1 =0 .2 mean2 = 5.3 sigma2 = 0.2 Correlation Coefficient, rho = 0.6 Given an x value of 6.3 (from dist1) what is the corresponding mean and standard deviation of y ? I can view the combined density function from the following: Mu = {mean1, mean2} CapSigma = {{sigma1^2, rho*sigma1*sigma2} , {rho, rho*sigma1*sigma2} dist = MultinormalDistribution[Mu,CapSigma] pdf = PDF[dist,{x,y}] plot1 = Plot3D[pdf, {x,4,7},{y,4,7}, PlotRange->All] but can't see how to determine the mean and the standard deviation of y for a given value of x, like 6.3 Any help would be appreciated. Thanks, --Steve