%-------------------------------------------------------------------------
%-------------------------------------------------------------------------
%   Drawing from densities
%-------------------------------------------------------------------------
%-------------------------------------------------------------------------
clear all;
clc;
%----------  # 1: Drawing from uniform and St.Normal %------------
N=50;
x.uniform=unifrnd(0,1,N,1);     %generate the sequence of random standard uniform variables
x.stand_normal=randn(N,1);      %generate the sequence of random standard normal variables
%---------- Plotting the histogram  --------------------------------------
%hist(x.uniform);               %lines are commented since we'll get all
%hist(x.stand_normal);          %the hisograms later on in a single graph

%----------  # 2: Generating Normal(2,9) -------------------------
mu=2;
sigma_sq=9;
x.normal=mu + sqrt(sigma_sq)*x.stand_normal;
%hist(x.normal);

%----------  # 3: Generating Log-Normal(-1,0.25) ------------------
mu=-1;
sigma_sq=0.25;
x.lognormal=exp(mu+sqrt(sigma_sq)*x.stand_normal);
%hist(x.lognormal);

%----------  # 4: Extreme value ----------------------------------
x.extreme=-log(-log(x.uniform))
%hist(x.extreme);

%----------  # 5: Truncated Normal with strictly negative values --------
%----------     Method i:  ------------------------
mu=2;
sigma_sq=9;
x.uniform=unifrnd(0,1,N,1);
x.truncated=norminv(normcdf(0,mu,sqrt(sigma_sq))*x.uniform);
%hist(x.truncated);

%----------     Method ii: Accept-Reject technique ------------------------
% works much slower than previous and given just for the sake of completeness
x.truncated1=zeros(N,1);
tries=100000;          %max number of tries to draw from N(2,9)
k=1;
    for i=1:tries;
        e=mu + sqrt(sigma_sq)*randn;
            if e<0
                x.truncated1(k)=e;
                k=k+1;
                    if k>N 
                        break
                    end;
            end;
    end;
if k<N
    fprintf('There was not enough tries to get all N observations\n');
end;

%---------- Plotting histograms --------
figure(2);
subplot(3,1,1);
hist(x.uniform);
title('Standard Uniform');
subplot(3,1,2);
hist(x.stand_normal);
title('Standard Normal');
subplot(3,1,3);
hist(x.normal);
title('Normal (2,9)');

figure(3);
subplot(3,1,1);
hist(x.lognormal);
title('Lognormal(-1.0.25)');
subplot(3,1,2);
hist(x.extreme);
title('Extreme Value');
subplot(3,1,3);
hist(x.truncated);
title('Truncated Normal(2,9)');

%---------- End of the file --------