Hey, I have a really simple question. How can I obtain a marginal density fx(x) from a joint distribution (x,y) ? In my case the joint distribution follows a log-normal distribution. I cannot use Quad since it requires both integrals (x and y). Thanks a lot for your help. Mo
MATLAB: Marginal Density from a joint DIstribution
joint distributionmarginal density
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Convolutions are pretty easy to do in Cupid. For example, the following code gives the attached figure
muX = 9.7224; % For Ni Distribution (X-domain)
sigmaX = 0.3332; % For Ni Distribution (X-domain)muY = 8.6878; % For Np Distribution (Y-domain)
sigmaY = 0.2454; % For Np Distribution (Y-domain)conv = Convolution(Lognormal(muX,sigmaX),Lognormal(muY,sigmaY));conv.PlotDensThis might be handy if you also want to try other distributions, try fitting data, etc.
From the integral that you use in order to calculate marginal PDFs, I guess that x,y are into the interval [0, +inf].
clearvars; clc; close all; syms x y Fxy(x,y) = 1-exp(-x)-exp(-y)+exp(-(x+y+x*y)); %Given CDF of X & Y
JPDFxy(x,y) = (x+y+x*y)*exp(-(x+y+x*y)); %Calculated Joint PDF of X & Y
MarginalPDFx(x) = int(JPDFxy,y,0,inf) %Formula for Marginal PDF of X
MarginalPDFy(y) = int(JPDFxy,x,0,inf) %Formula for Marginal PDF of Y
r=0:0.1:10; %plot PDFs for 0<x,y<10
pdfx=zeros(size(r)); pdfy=zeros(size(r)); for n=1:length(r) pdfx(n)=MarginalPDFx(r(n)); pdfy(n)=MarginalPDFy(r(n)); end figure; subplot(2,1,1); plot(r,pdfx,'-b'); grid on; legend('PDFx'); subplot(2,1,2); plot(r,pdfy,'-r'); grid on; legend('PDFy');Since Fxy is symmetrical, two PDFs are indentical:
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