function F = spm_Xcdf(x,v)
% Cumulative Distribution Function (CDF) of Chi-squared distribution
% FORMAT F = spm_Xcdf(x,v)
%
% x - Chi-squared variate
% v - degrees of freedom (v>0, non-integer d.f. accepted)
% F - CDF at x of Chi-squared distribution with v degrees of freedom
%__________________________________________________________________________
%
% spm_Xcdf implements the Cumulative Distribution of Chi-squared
% distributions.
%
% Returns the probability p, that a Students Chi-squared variate on v
% degrees of freedom is less than x. F(x) = Pr{X<x} for X~\Chi^2(v)
%
% Definition:
%--------------------------------------------------------------------------
% The Chi-squared distribution with v degrees of freedom is defined for
% positive integer v and x in [0,Inf). The Cumulative Distribution
% Function (CDF) F(x) is the probability that a realisation of a
% Chi-squared random variable X has value less than x. F(x)=Pr{X<x}:
% (See Evans et al., Ch8)
%
% Variate relationships: (Evans et al., Ch8 & Ch18)
%--------------------------------------------------------------------------
% The Chi-squared distribution with v degrees of freedom is equivalent to
% the Gamma distribution with scale parameter 1/2 and shape parameter v/2.
%
% Algorithm:
%--------------------------------------------------------------------------
% Using routine spm_Gcdf for Gamma distribution, with appropriate parameters.
%
% References:
%--------------------------------------------------------------------------
% Evans M, Hastings N, Peacock B (1993)
%       "Statistical Distributions"
%        2nd Ed. Wiley, New York
%
% Abramowitz M, Stegun IA, (1964)
%       "Handbook of Mathematical Functions"
%        US Government Printing Office
%
% Press WH, Teukolsky SA, Vetterling AT, Flannery BP (1992)
%       "Numerical Recipes in C"
%        Cambridge
%
%__________________________________________________________________________
% Copyright (C) 1992-2011 Wellcome Trust Centre for Neuroimaging

% Andrew Holmes
% $Id: spm_Xcdf.m 4182 2011-02-01 12:29:09Z guillaume $


%-Check enough arguments
%--------------------------------------------------------------------------
if nargin<2, error('Insufficient arguments'), end

%-Computation
%--------------------------------------------------------------------------
F = spm_Gcdf(x,v/2,1/2);