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normcdflog

PURPOSE ^

NORMCDFLOG calculates log of Normal Cumulative Distribution function p=(x,m,s)

SYNOPSIS ^

function p=normcdflog(x,m,s)

DESCRIPTION ^

NORMCDFLOG calculates log of Normal Cumulative Distribution function p=(x,m,s)

 Inputs: 

     X        Input data (vector or matrix)
     M        Mean of Normal distribution [default 0]
     S        Std deviation of Normal distribution [default 1]

 Outputs: 

     P        P = log(normcdf(X)); same size as X

 The routine gives accurate values even if X is large and negative

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function p=normcdflog(x,m,s)
0002 %NORMCDFLOG calculates log of Normal Cumulative Distribution function p=(x,m,s)
0003 %
0004 % Inputs:
0005 %
0006 %     X        Input data (vector or matrix)
0007 %     M        Mean of Normal distribution [default 0]
0008 %     S        Std deviation of Normal distribution [default 1]
0009 %
0010 % Outputs:
0011 %
0012 %     P        P = log(normcdf(X)); same size as X
0013 %
0014 % The routine gives accurate values even if X is large and negative
0015 
0016 %      Copyright (C) Mike Brookes 2016
0017 %      Version: $Id: normcdflog.m 8839 2016-10-19 15:03:19Z dmb $
0018 %
0019 %   VOICEBOX is a MATLAB toolbox for speech processing.
0020 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
0021 %
0022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0023 %   This program is free software; you can redistribute it and/or modify
0024 %   it under the terms of the GNU General Public License as published by
0025 %   the Free Software Foundation; either version 2 of the License, or
0026 %   (at your option) any later version.
0027 %
0028 %   This program is distributed in the hope that it will be useful,
0029 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0030 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0031 %   GNU General Public License for more details.
0032 %
0033 %   You can obtain a copy of the GNU General Public License from
0034 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0035 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0037 persistent a b
0038 if isempty(a)
0039     a=0.996;
0040 %   f=@(x) -0.5*(x.^2+log(2*pi))-real(log(-(a+x.^2)./x))-real(log(normcdf(x)));
0041 %   b=fzero(f,-22);         % cutoff value for conventional formula
0042     b=-22.2491306156561;    % precalculated value
0043 end
0044 if nargin>2
0045     x=(x-m)/s;
0046 elseif nargin>1
0047     x=x-m;
0048 end
0049 t=x<b;                                                  % mask for large negative values
0050 p=zeros(size(x));
0051 p(~t)=real(log(0.5*erfc(-x(~t).*sqrt(0.5))));           % use this formula normally
0052 p(t)=-0.5*(x(t).^2+log(2*pi))-real(log(-x(t)-a./x(t))); % use this approximation for large negative x
0053

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