# v_lognmpdf

## PURPOSE

V_LOGNMPDF calculate pdf of a multivariate lognormal distribution P=(X,M,V)

## SYNOPSIS

function p=v_lognmpdf(x,m,v)

## DESCRIPTION

```V_LOGNMPDF calculate pdf of a multivariate lognormal distribution P=(X,M,V)

Inputs:  X(N,D)   are the points at which to calculate the pdf (one point per row)
M(D)     is the mean vector of the distribution [default M = ones]
V(D,D)   is the covariance matrix of the distribution. If V is diagonal
it may be given as a vector [default V = identity matrix]

Outputs:  P(N,1)   is the pdf at each row of X

Example: lognmpdf(linspace(0,10,1000)',2);```

## CROSS-REFERENCE INFORMATION

This function calls:
• v_pow2cep V_POW2CEP convert power domain means and variances to the cepstral domain
This function is called by:

## SOURCE CODE

```0001 function p=v_lognmpdf(x,m,v)
0002 %V_LOGNMPDF calculate pdf of a multivariate lognormal distribution P=(X,M,V)
0003 %
0004 %  Inputs:  X(N,D)   are the points at which to calculate the pdf (one point per row)
0005 %           M(D)     is the mean vector of the distribution [default M = ones]
0006 %           V(D,D)   is the covariance matrix of the distribution. If V is diagonal
0007 %                    it may be given as a vector [default V = identity matrix]
0008 %
0009 % Outputs:  P(N,1)   is the pdf at each row of X
0010 %
0011 % Example: lognmpdf(linspace(0,10,1000)',2);
0012
0013 %       Copyright (C) Mike Brookes 1995
0014 %      Version: \$Id: v_lognmpdf.m 10865 2018-09-21 17:22:45Z dmb \$
0015 %
0016 %   VOICEBOX is a MATLAB toolbox for speech processing.
0018 %
0019 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0020 %   This program is free software; you can redistribute it and/or modify
0022 %   the Free Software Foundation; either version 2 of the License, or
0023 %   (at your option) any later version.
0024 %
0025 %   This program is distributed in the hope that it will be useful,
0026 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0027 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0028 %   GNU General Public License for more details.
0029 %
0030 %   You can obtain a copy of the GNU General Public License from
0031 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0032 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0033 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0034
0035 if nargin<3
0036     if nargin<2
0037         m=ones(1,size(x,2));
0038     end
0039     v=eye(length(m));
0040 end
0041 if(size(x,2)~=length(m)) | (size(x,2)~=length(v))
0042     error('Number of columns must match mean and variance dimensions');
0043 end
0044 [u,k]=v_pow2cep(m,v,'i'); % convert to log domain
0045 p=zeros(size(x,1),1);
0046 c=prod(x,2);
0047 q=c>0;
0048 p(q)=mvnpdf(log(x(q,:)),u,k)./c(q);
0049
0050 if ~nargout & (length(u)==1)
0051     plot(x,p);
0052 end```