# Gaussian Kernel Density Estimation Demonstration

Several examples show how to use the gkdeb function.

## 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
```