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# v_vonmisespdf

## PURPOSE

V_VONMISESPDF Von Mises probability distribution P=(x,m,k)

## SYNOPSIS

function p=v_vonmisespdf(x,m,k)

## DESCRIPTION

V_VONMISESPDF Von Mises probability distribution P=(x,m,k)

Inputs:  X         matrix of input values (in radians)
M         mean angle of distribution (in radians)
K         concentration parameter

Outputs:  P         matrix of probability density values (same size as X)
(with no output argument, the function will plot a graph)

The von Mises distribution describes the pdf of an angle over the range [0,2pi).
For large K, the distribution approximates a Gaussian with mean M and
variance 1/K. For small K, the distribution is uniform.

## CROSS-REFERENCE INFORMATION

This function calls:
• v_axisenlarge V_AXISENLARGE - enlarge the axes of a figure (f,h)
• v_vonmisespdf V_VONMISESPDF Von Mises probability distribution P=(x,m,k)
This function is called by:
• v_vonmisespdf V_VONMISESPDF Von Mises probability distribution P=(x,m,k)

## SOURCE CODE

0001 function p=v_vonmisespdf(x,m,k)
0002 %V_VONMISESPDF Von Mises probability distribution P=(x,m,k)
0003 %
0004 %  Inputs:  X         matrix of input values (in radians)
0005 %           M         mean angle of distribution (in radians)
0006 %           K         concentration parameter
0007 %
0008 % Outputs:  P         matrix of probability density values (same size as X)
0009 %                     (with no output argument, the function will plot a graph)
0010 %
0011 % The von Mises distribution describes the pdf of an angle over the range [0,2pi).
0012 % For large K, the distribution approximates a Gaussian with mean M and
0013 % variance 1/K. For small K, the distribution is uniform.
0014
0015 %      Copyright (C) Mike Brookes 1997-2011
0016 %      Version: $Id: v_vonmisespdf.m 10865 2018-09-21 17:22:45Z dmb$
0017 %
0018 %   VOICEBOX is a MATLAB toolbox for speech processing.
0020 %
0021 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0022 %   This program is free software; you can redistribute it and/or modify
0024 %   the Free Software Foundation; either version 2 of the License, or
0025 %   (at your option) any later version.
0026 %
0027 %   This program is distributed in the hope that it will be useful,
0028 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0029 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0030 %   GNU General Public License for more details.
0031 %
0032 %   You can obtain a copy of the GNU General Public License from
0033 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0034 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0035 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0036 if nargout>0
0037     p=exp(k*cos(x-m))/(2*pi*besseli(0,k));
0038 else
0039     if nargin<1 || isempty(x)
0040         x=linspace(-pi,pi,181);
0041     end
0042     if nargin<2 || isempty(m)
0043         m=0;
0044     end
0045     if nargin<3 || isempty(k)
0046         k=[0 pow2(-1:3)];
0047     end
0048     nm=length(m);
0049     nk=length(k);
0050     np=max(nm,nk);
0051     pp=zeros(length(x),np);
0052     pl=cell(np,1);
0053     for i=1:np
0054         mi=m(1+rem(i-1,nm));
0055         ki=k(1+rem(i-1,nk));
0056         pp(:,i)=v_vonmisespdf(x(:),mi,ki);
0057         pl{i}=sprintf('\\mu=%.1f, \\kappa=%.1f',mi,ki);
0058     end
0059     plot(x,pp);
0060     v_axisenlarge([-1 -1.05]);
0061     legend(pl,'location','northeast');
0062 end
0063