# Bivariate Kernel Density Estimation Demonstration

Several examples show how to use the gkdeb2 function.

## 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);
```  