% PLOT_APD_PDF_SURF.M     
%   PLOTAPDPDFSURF.M plots the surfaces corresponding to the pdfs of an APD 
%   random variable with parameters ALPHA and LDA. 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

% Inputs the values of lda
lda = [0.8;1;2;4];

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

% First define X and Y axis: X = x and Y = alpha
alpha = [((1/Nprec):(2/Nprec):0.5)';0.5;((0.5+1/Nprec):(2/Nprec):(1-1/Nprec))'];
x = (-5:(10/Nprec):5)';
y = alpha;
resden = zeros(size(x,1),size(alpha,1),size(lda,1));
for j = 1:1:size(lda,1)
    den = [];
    for i = 1:1:size(alpha,1)
        d = APDpdf(alpha(i)*ones(size(x)),lda(j)*ones(size(x)),x);
        den = [den,d]; 
    end
    resden(:,:,j) = den;
end
subplot(2,2,1);
surf(x,alpha,resden(:,:,1)');
colormap hsv; 
axis([-5 5 0 1 0 0.6]);
title('Lambda = 0.8');

subplot(2,2,2);
surf(x,alpha,resden(:,:,2)');
colormap hsv;
axis([-5 5 0 1 0 0.6]);
title('Lambda = 1');

subplot(2,2,3);
surf(x,alpha,resden(:,:,3)');
colormap hsv;
axis([-5 5 0 1 0 0.6]);
title('Lambda = 2');

subplot(2,2,4);
surf(x,alpha,resden(:,:,4)');
colormap hsv;
axis([-5 5 0 1 0 0.6]);
title('Lambda = 4');