% x = vector specifying random variables.
% y = vector specifying points for which CDF and PDF has to be evaluated.  
% The CDF is evaluated using the data in the vector x above, 
% at the points in y.
close all
clear all
n = 500;
param1 = [-0.0936 , 1.27 *10^(-6)  , 0.6145];
al = param1(1) ; th = param1(2) ; de = param1(3) ;
x = twdrnd(al,th,de,n);
y  = linspace(0,max(x));
ny = length(y);
nx = length(x);
for i = 1:ny
p = 0;              % True  Probability
q = 0;              % False Probability
for j = 1:nx
if x(j)<=y(i)   % Definition of CDF
p = p + 1;
else
q = q + 1;
end
end
F(i) = p/(p + q);   % Calulating Probability
end
plot(y,F,'o');
% Now a faster and more compact version of the previous definition
x1  = unique(x); % in principle duplicates should be removed
nx = length(x1);
y1  = linspace(0,max(x1));
ny = length(y1);
sump = sum(x1<=y1 , 1);
FF = sump/nx;
hold on;
plot(y1,FF,'-r')
legend('CDF using loops' , 'CDF using vectorization');
title({'CDF computed using definition' , '$F(x) = (\sum (I(X<=x)))/(n)$'},'interpreter','latex','Fontsize',16);
% both definitions above are along the matlab fiunction cdfplot(x)