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# wnormndpdf

## PURPOSE

N-Dimensional Normal probability density function.

## SYNOPSIS

pdf = wnormndpdf(X,m,S)

## DESCRIPTION

``` WNORMNDPDF N-Dimensional Normal probability density function.

CALL: pdf = wnormndpdf(X,m,S)

X = matrix of evaluation points
m = mean              (default zero vector)
S = Covariance matrix (default identity matrix)

Example: % Bivariate Gaussian distribution
x = linspace(-5,5);
[X1 X2] = meshgrid(x);
f = reshape(wnormndpdf([X1(:),X2(:)]),100,100);
[area,epsi] = simpson(x,f);
[area2,epsi2] = simpson(x,area);

## CROSS-REFERENCE INFORMATION

This function calls:
 det Determinant. error Display message and abort function. inv Matrix inverse. sprintf Write formatted data to string.
This function is called by:

## SOURCE CODE

```001 function pdf = wnormndpdf(X,m,S)
002 %WNORMNDPDF N-Dimensional Normal probability density function.
003 %
004 % CALL: pdf = wnormndpdf(X,m,S)
005 %
006 %   X = matrix of evaluation points
007 %   m = mean              (default zero vector)
008 %   S = Covariance matrix (default identity matrix)
009 %
010 % Example: % Bivariate Gaussian distribution
011 % x = linspace(-5,5);
012 % [X1 X2] = meshgrid(x);
013 % f = reshape(wnormndpdf([X1(:),X2(:)]),100,100);
014 % [area,epsi] = simpson(x,f);
015 % [area2,epsi2] = simpson(x,area);
016 %
018
019 %History
020 % Revised pab 11nov2003
021 % By pab 2002
022 error(nargchk(1,3,nargin))
023
024
025 [n,d]=size(X);
026
027 if nargin<2|isempty(m),
028   m = zeros(1,d);
029 end
030 if nargin<3|isempty(S),
031   S = eye(d);
032 end
033 if any(d~=size(S))
034   error(sprintf('Covariance matrix must have %d dimensions',d))
035 end
036
037
038
039 den = (2*pi*det(S))^(d/2);
040 if den< eps,
041   error('Covariance matrix singular')
042 end
043 Xn = X-m(ones(n,1),:);
044 pdf = zeros(n,1);
045 S1 = inv(S);
046 if 1, % new and fast call
047   pdf = exp(-0.5*sum((Xn(:,:)*S1).*Xn(:,:) ,2))/den;
048 else
049   % old call slow
050   for ix=1:n
051     pdf(ix) = exp(-0.5*Xn(ix,:)*S1*(Xn(ix,:).'))/den;
052   end
053 end```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group

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