spm_Ncdf_jdw.m
e5f5005bb2efmaster

spm_Ncdf_jdw.m
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			function F = spm_Ncdf_jdw(x,u,v)
			% Cumulative Distribution Function (CDF) for univariate Normal distributions: J.D. Williams aproximation
			% FORMAT F = spm_Ncdf_jdw(x,u,v)
			%
			% x - ordinates
			% u - mean [Defaults to 0]
			% v - variance (v>0) [Defaults to 1]
			% F - pdf of N(u,v) at x (Lower tail probability)
			%__________________________________________________________________________
			%
			% spm_Ncdf implements the Cumulative Distribution Function (CDF) for
			% the Normal (Gaussian) family of distributions.
			%
			% References:
			%--------------------------------------------------------------------------
			% An Approximation to the Probability Integral
			% J. D. Williams
			% The Annals of Mathematical Statistics, Vol. 17, No. 3. (Sep., 1946), pp.
			% 363-365.
			%
			%__________________________________________________________________________
			% Copyright (C) 2008 Wellcome Trust Centre for Neuroimaging

			% Karl Friston
			% $Id: spm_Ncdf_jdw.m 4836 2012-08-10 15:55:21Z karl $


			%-Format arguments
			%--------------------------------------------------------------------------
			if nargin < 3, v = 1; end
			if nargin < 2, u = 0; end

			%-Approximate integral
			%--------------------------------------------------------------------------
			x = (x - u)./sqrt(abs(v));
			F = sqrt(1 - exp(-(2/pi)*x.^2))/2;
			i = x < 0;
			F(i) = -F(i);
			F = F + 1/2;