% PLOT_APD_STAT.M     
%   PLOTAPDSTAT.M plots the 2D-graphs corresponding to the first four moments of 
%   an Asymetric Power Distributed (APD) random variable. 
%   Here LDA is held fixed and ALPHA varies in (0,1).
%
% Comments: 
%   a standard APD(alpha,lda) random variable X has probability density:
%   p(alpha,lda,x) = [A^(1/lda)/gamma(1+1/lda)]*...
%                   *exp[-(A/alpha^lda)*abs(x)^lda],        if x <= 0,
%                   *exp[-(A/(1-alpha)^lda)*abs(x)^lda],    if x > 0,
%   where A = (2*alpha^lda*(1-alpha)^lda)/(alpha^lda+(1-alpha)^lda).
%
% References:
%   [1] Komunjer, I. (2006): "Asymmetric Power Distribution: Theory and 
%   Applications to Risk Measurement"
%
% Author: Ivana Komunjer - UCSD (komunjer@ucsd.edu)
% Version: 2.1        Date: 06/07/2006

% Controls the precision of the plot
Nprec = 51;        % number of points on the grid

% First define X and Y axis: X = alpha and Y = lda
m1 = []; m2 = []; m3 = []; m4 = [];
alpha = [((1/Nprec):(1/Nprec):0.5)';0.5;((0.5+1/Nprec):(1/Nprec):(1-1/Nprec))'];
lda = [0.7;1;2;4];
x = alpha;
for i = 1:1:size(lda,1)
    m = APDstat(alpha,lda(i)*ones(size(alpha)));
    m1 = [m1,m(:,1)]; m2 = [m2,m(:,2)]; m3 = [m3,m(:,3)]; m4 = [m4,m(:,4)];
end
subplot(2,2,1);
hold on;
for i=1:1:size(lda,1)
    plot(alpha,m1(:,i));
    axis([0 1 -5 5]);
end
hold off;
title('Mean');

subplot(2,2,2);
hold on;
for i=1:1:size(lda,1)
    plot(alpha,m2(:,i));
    axis([0 1 0 20]);
end
hold off;
title('Variance');

subplot(2,2,3);
hold on;
for i=1:1:size(lda,1)
    plot(alpha,m3(:,i));
    axis([0 1 -3 3]);
end
hold off;
title('Skewness');

subplot(2,2,4);
hold on;
for i=1:1:size(lda,1)
    plot(alpha,m4(:,i));
    axis([0 1 2 20]);
end
hold off;
title('Kurtosis');