echo on
% First, use the transformation method:
N = 100000;
Z = rand(N,1);
delta = 0.05
bins = [0:delta:10];
Y = (Z<0.5).*sqrt(2*Z) + (Z>=0.5).*(2-sqrt(abs(2-2*Z)));
[p,tmp] = hist(Y,bins);
plot(bins,p/N/delta,[0 1 2], [0 1 0]);
title('Transforming uniform to triangle');
legend('Histogram of transformed uniform','True exponential pdf')

pause;

% Now, use the sum of two uniforms method (convolution theorem):
Z = rand(N,1);
X = rand(N,1);
Y = Z + X;
[p,tmp] = hist(Y,bins);
plot(bins,p/N/delta, [0 1 2], [0 1 0]);
title('Transforming uniform to triangle');
legend('Histogram of transformed uniform','True exponential pdf')

pause

% Now, generate exponetial distribution from uniform
N = 1e5;
delta = 0.05
bins = [0:delta:10];
Z = rand(N,1);
Y = -log(1-Z);
[p,tmp] = hist(Y,[0:delta:10]);
plot(bins,p/N/delta, bins, exp(-bins));
title('Transforming uniform to exponential');
legend('Histogram of transformed uniform','True exponential pdf')


echo off