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Bivariant Kernel Density Estimation (V2.1)

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20 Mar 2008 (Updated )

A tool for bivariant pdf, cdf and icdf estimation using Gaussian kernel function.

Bivariate Kernel Density Estimation Demonstration

Bivariate Kernel Density Estimation Demonstration

Several examples show how to use the gkdeb2 function.

Contents

Distribution with unbounded support

Distribution with four peaks.

x = [randn(100,1), (randn(100,1)-10)*2;
      randn(100,1)+10, randn(100,1);
      randn(100,1)+10, (randn(100,1)-10)*2;
      randn(100,2)];
gkde2(x);

Distribution with upper and lower bounds: uniform distribution

clear
x=rand(10000,2);
% PDF with bounded support
p.xylim=[0 0 1 1];
gkde2(x,p);
% Compare with unbounded PDF estimate
figure;
gkde2(x);

Distribution with lower bound only: exponential distribution

clear
x=-log(rand(1000,2));
% PDF with bounded support
p.xylim=[0 0 Inf Inf];
gkde2(x,p);
% Compare with unbounded PDF estimate
figure
gkde2(x);

Distribution with lower bound only: log-normal distribution

clear
x=exp(randn(1000,2));
% PDF with bounded support
p.xylim=[0 0 Inf Inf];
gkde2(x,p);
% Compare with unbounded PDF estimate
figure
gkde2(x);

Distribution with lower bound only: chi-square distribution

clear
x=randn(1000,2).^2;
% PDF with bounded support
p.xylim=[0 0 Inf Inf];
p.alpha=0.95;
gkde2(x,p);
% Compare with unbounded PDF estimate
figure
p1.alpha=0.95;
gkde2(x,p1);

Distribution with lower bound only: Rayleigh distribution

clear
x=sqrt(randn(2,1000).^2 + randn(2,1000).^2);
% PDF with bounded support
p.xylim=[0 0 Inf Inf];
p.alpha=0.95;
gkde2(x,p);
% Compare with unbounded PDF estimate
figure
p1.alpha=0.95;
gkde2(x,p1);

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