function PhiValue = PhiFunction(a)
% PhiFunction: Calculates the value of the cumulative normal distribution from minus infinity to a.
%
% USAGE:
%
%       PhiValue = PhiFunction(a)
%
% REQUIRED INPUT:  a (vector) with real values.
%
% REQUIRED OUTPUT: PhiValue (vector) with probabilities that a standard normal random variable
%                           takes values equal to or less than a.
%
%
%                       Written by: Anders Warne
%                                   New Area Wide Model Project
%                                   DG-R/EMO
%                                   European Central Bank (ECB)
%                                   Email: anders.warne@ecb.europa.eu
%                                   Copyright © 2006-2008 European Central Bank.
%
%                       First version: July 14, 2006.
%                        This version: December 18, 2008.
%
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%
% LICENSE INFORMATION:
%
%      YADA is free software: you can redistribute it and/or modify
%      it under the terms of the GNU General Public License as published by
%      the Free Software Foundation, either version 3 of the License, or
%      (at your option) any later version.
%
%      This program is distributed in the hope that it will be useful,
%      but WITHOUT ANY WARRANTY; without even the implied warranty of
%      MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%      GNU General Public License for more details.
%
%      You should have received a copy of the GNU General Public License
%      along with this program.  If not, see <http://www.gnu.org/licenses/>.
%
%      YADA is released under the GNU General Public License, Version 3,
%      29 June 2007 <http://www.gnu.org/licenses/>. The current release of
%      the program was last modified by the ECB on the "This version" date
%      above.
%
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%
% CHANGELOG:
%
% * 17-7-2006:  Fixed the call to the sqrt function [Used LaTeX code in firts version ;)]
%
% * 19-7-2006:  Updated function information.
%
% * 25-8-2006:  The function now accepts a vector.
%
% * 28-8-2006:  Updated the documentation.
%
% * 13-11-2007: Updated the documentation.
%
% * 23-5-2008:  Updated the documentation.
%
% * 9-7-2008:   Fixed a bug where last PhiValue was expressed as Phivalue.
%
% * 18-12-2008: Updated the documentation.
%
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%

PhiValue = zeros(size(a));
PhiValue(a>0) = (1/2) + ((1/2)*erf(a(a>0)/sqrt(2)));
PhiValue(a<=0) = (1/2) - ((1/2)*erf(-a(a<=0)/sqrt(2)));

%
% end of PhiFunction.m
%
