% crv.m - plot various continuous random variable pdfs
% (C) copyright 2001 by Yu Hen Hu
% Created: 2/17/2001

clear all,

% Uniform distribution
a = 0; b = 2; dx=0.01;
x=[a-0.5:dx:b+0.5];
f=[a <= x & x <= b]/(b-a);
figure(1),subplot(231),
plot(x,f), title(['uniform[' num2str(a) ',' num2str(b) ']']);
axis([min(x) max(x) 0 max(f)*1.1]);
cdf=f*triu(ones(length(x),length(x)))*dx;
figure(2),subplot(231),
plot(x,cdf), title(['CDF: uniform[' num2str(a) ',' num2str(b) ']']);
axis([min(x) max(x) 0 max(cdf)*1.1]);


% exponential distribution
lambda=0.2; dx=0.05;
x=[-1:dx:5/lambda];
f=[x>=0].*exp(-lambda*x)*lambda;
figure(1),subplot(232),
plot(x,f), title(['exp(' num2str(lambda) ')']);
axis([min(x) max(x) 0 max(f)*1.1]);
cdf=f*triu(ones(length(x),length(x)))*dx;
figure(2),subplot(232),
plot(x,cdf), title(['CDF: exp(' num2str(lambda) ')']);
axis([min(x) max(x) 0 max(cdf)*1.1]);

% Laplace pdf
lambda=1; dx=0.05;
x=[-5/lambda:dx:5/lambda];
f=0.5*lambda*exp(-lambda*abs(x));
figure(1),subplot(233),
plot(x,f), title(['Laplace(' num2str(lambda) ')']);
axis([min(x) max(x) 0 max(f)*1.1]);
cdf=f*triu(ones(length(x),length(x)))*dx;
figure(2),subplot(233),
plot(x,cdf), title(['CDF: Laplace(' num2str(lambda) ')']);
axis([min(x) max(x) 0 max(cdf)*1.1]);

% Cauchy pdf
lambda=1; dx=0.05;
x=[-5/lambda:dx:5/lambda];
f=(lambda/pi)*ones(1,length(x))./(lambda^2+x.*x);
figure(1),subplot(234),
plot(x,f), title(['Cauchy(' num2str(lambda) ')']);
axis([min(x) max(x) 0 max(f)*1.1]);
cdf=f*triu(ones(length(x),length(x)))*dx;
figure(2),subplot(234),
plot(x,cdf), title(['CDF: Cauchy(' num2str(lambda) ')']);
axis([min(x) max(x) 0 max(cdf)*1.1]);

% Gaussian pdf
m = 1; sigma=.4; dx=0.05;
x=[-5*sigma:dx:5*sigma]+m;
f=(1/(sqrt(2*pi)*sigma))*exp(-(0.5/sigma^2)*(x-m).*(x-m));
figure(1),subplot(235),
plot(x,f), title(['Gaussian(' num2str(m) ',' num2str(sigma^2) ')']);
axis([min(x) max(x) 0 max(f)*1.1]);
cdf=f*triu(ones(length(x),length(x)))*dx;
figure(2),subplot(235),
plot(x,cdf), title(['CDF: Gaussian(' num2str(m) ',' num2str(sigma^2) ')']);
axis([min(x) max(x) 0 max(cdf)*1.1]);