Gaussian Kernel Density Estimation Demonstration

Several examples show how to use the gkdeb function.

Contents

• Distribution with unbounded support
• Distribution with upper and lower bounds: uniform distribution
• Distribution with lower bound only: exponential distribution
• Distribution with lower bound only: log-normal distribution
• Distribution with lower bound only: chi-square distribution
• Distribution with lower bound only: Rayleigh distribution

Distribution with unbounded support

Distribution with two peaks.

x = [0.1*randn(50,1); randn(50,1)+6];
gkdeb(x);

Distribution with upper and lower bounds: uniform distribution

clear
x=rand(10000,1);
% PDF with bounded support
p.lB=0;
p.uB=1;
fhandle=figure;
gkdeb(x,p);
% Compare with unbounded PDF estimate
p=gkdeb(x);
figure(fhandle)
subplot(211)
hold
plot(p.x,p.pdf,'r--','linewidth',2);
axis([-0.5 1.5 0 1.1])
legend('Bounded','Unbounded','Location','South')
subplot(212)
hold
plot(p.x,p.cdf,'r--','linewidth',2);
axis([-0.5 1.5 0 1.1])
legend('Bounded','Unbounded','Location','SouthEast')

Current plot held
Current plot held

Distribution with lower bound only: exponential distribution

clear
x=-log(rand(1000,1));
% PDF with bounded support
p.lB=0;
p.uB=inf;
fhandle=figure;
gkdeb(x,p);
% Compare with unbounded PDF estimate
p=gkdeb(x);
figure(fhandle)
subplot(211)
hold
plot(p.x,p.pdf,'r--','linewidth',2);
axis([-1 10 0 1])
legend('Bounded','Unbounded','Location','East')
subplot(212)
hold
plot(p.x,p.cdf,'r--','linewidth',2);
axis([-1 10 0 1])
legend('Bounded','Unbounded','Location','East')

Current plot held
Current plot held

Distribution with lower bound only: log-normal distribution

clear
x=exp(randn(1000,1));
% PDF with bounded support
p.lB=0;
p.uB=inf;
fhandle=figure;
gkdeb(x,p);
% Compare with unbounded PDF estimate
p=gkdeb(x);
figure(fhandle)
subplot(211)
hold
plot(p.x,p.pdf,'r--','linewidth',2);
axis([-1 10 0 1])
legend('Bounded','Unbounded','Location','East')
subplot(212)
hold
plot(p.x,p.cdf,'r--','linewidth',2);
axis([-1 10 0 1])
legend('Bounded','Unbounded','Location','East')

Current plot held
Current plot held

Distribution with lower bound only: chi-square distribution

clear
x=randn(1000,1).^2;
% PDF with bounded support
p.lB=0;
p.uB=inf;
p.alpha=0.95;
fhandle=figure;
gkdeb(x,p);
% Compare with unbounded PDF estimate
p=gkdeb(x);
figure(fhandle)
subplot(211)
hold
plot(p.x,p.pdf,'r--','linewidth',2);
axis([-1 10 0 1])
legend('Bounded','Unbounded','Location','East')
subplot(212)
hold
plot(p.x,p.cdf,'r--','linewidth',2);
axis([-1 10 0 1])
legend('Bounded','Unbounded','Location','East')

Current plot held
Current plot held

Distribution with lower bound only: Rayleigh distribution

clear
x=sqrt(randn(1,1000).^2 + randn(1,1000).^2);
% PDF with bounded support
p.lB=0;
p.uB=inf;
p.alpha=0.95;
fhandle=figure;
gkdeb(x,p);
% Compare with unbounded PDF estimate
p=gkdeb(x);
figure(fhandle)
subplot(211)
hold
plot(p.x,p.pdf,'r--','linewidth',2);
axis([-1 7 0 1])
legend('Bounded','Unbounded','Location','East')
subplot(212)
hold
plot(p.x,p.cdf,'r--','linewidth',2);
axis([-1 7 0 1])
legend('Bounded','Unbounded','Location','East')

Current plot held
Current plot held

Published with MATLAB® 7.10