function f = APDcdf(alpha,lda,x);
% APDCDF.M     Asymmetric Power Distribution (APD) cumulative distribution function
%   F = APDCDF(ALPHA,LDA,X) computes the cdf of a standard APD random variable
%   with parameters ALPHA, 0 < ALPHA < 1, and LDA, LDA > 0, and evaluated at 
%   some real value X. 
%
% Inputs:
%   ALPHA = Nx1-vector of shape parameter alpha, 0 < ALPHA(n) < 1, for 1 <= n <= N; 
%   LDA = Nx1-vector of shape parameter lda, LDA(n) > 0 for 1 <= n <= N;
%   X = Nx1-vector of real values.
%
% Outputs:
%   F = Nx1-vector of APD(ALPHA(n),LDA(n)), 1 <= n <= N, cdf evaluated at X;
%
% 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

if nargin < 3, 
    error('Requires three input arguments'); 
end

[errorcode alpha lda x] = distchck(3,alpha,lda,x);

if errorcode > 0
    error('Requires non-scalar arguments to match in size.');
end

% Computes A
a = 2*(alpha.^lda).*((1-alpha).^lda)./(alpha.^lda+(1-alpha).^lda);

% Initialize f to zero.
f = zeros(size(a));

%   Return NaN if the arguments ALPHA and LDA are outside their limits.
f(alpha<=0 | alpha>=1 | lda<=0,:) = NaN;     

k = find(alpha>0 & alpha<1 & lda>0);
ak = a(k); ldak = lda(k); alphak = alpha(k); xk = x(k); onek = ones(size(ak));
if any(k)
    fk = (xk<=0).*alphak.*(1-gammainc((ak.*(abs(xk)).^ldak)./(alphak.^ldak),1./ldak)) +...
        (xk>0).*(1-(1-alphak).*(1-gammainc((ak.*(abs(xk)).^ldak)./((1-alphak).^ldak),1./ldak)));
end

f(k) = fk;

% Make sure that round-off errors never make f less than 0 or greater than 1.
f(f < 0) = 0;
f(f > 1) = 1;