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# estmc

## PURPOSE

estimates transition matrix P from a time series of a Markov chain.

## SYNOPSIS

[Pest,N,Ni] = estmc(z,r)

## DESCRIPTION

ESTMC  estimates transition matrix P from a time series of a Markov chain.

[Pest,N] = estmc(z,r);

z    = time series of a Markov chain.    [1xT]
r    = number of states in Markov chain.

Pest = Estimated transition matrix.
N    =

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
 itmkurs_lab2 Script to computer exercises 2 test_markov Quick test of the routines in module 'markov'

## SOURCE CODE

001 function [Pest,N,Ni] = estmc(z,r)
002 % ESTMC  estimates transition matrix P from a time series of a Markov chain.
003 %
004 % [Pest,N] = estmc(z,r);
005 %
006 % z    = time series of a Markov chain.    [1xT]
007 % r    = number of states in Markov chain.
008 %
009 % Pest = Estimated transition matrix.
010 % N    =
011
012
013 T = length(z);
014
015 N = zeros(r,r);
016 Pest = zeros(r,r);
017
018 for i = 1:r
019   for j=1:r
020     N(i,j) = sum( (z(1:T-1)==i) & (z(2:T)==j) );
021 %    if i==j
022 %      N(i,i) = sum(z(1:T-1)==i);
023 %    else
024 %      N(i,j) = sum((z(2:T)-z(1:T-1))==j-i);
025 %    end
026   end
027 end
028
029 Ni = sum(N,2);
030
031 for i = 1:r
032   if Ni(i) > 0
033     Pest(i,:) = N(i,:)/Ni(i);
034   else
035     Pest(i,:) = ones(1,r)/r;
036   end
037   Pest(i,i) = 0;
038   Pest(i,i) = 1-sum(Pest(i,:));
039 end
040
041
042
043

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

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