Gives the stationary probabilities for a 1st-order Markov chain (R.P. Littlejohn).
Option
PRINT = string token |
What to print (transitions , pstationary ); default psta |
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Parameters
DATA = matrices or factors | Specifies the Markov chain as a factor, or matrix of transitions |
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STATES = texts |
Labels for the states |
PSTATIONARY = variates |
Saves the stationary probabilities |
TRANSITIONS = matrices |
Saves the transition matrices |
Description
MC1PSTATIONARY
prints and/or saves the stationary probabilities for a first-order Markov chain. The data are input using the DATA
parameter, as either a matrix of transition counts or a factor of states from which the transition matrix is calculated. The probabilities and transition matrix can be saved using the TRANSITIONS
and PSTATIONARY
parameters, respectively.
Option: PRINT
.
Parameters: DATA
, STATES
, PSTATIONARY
, TRANSITIONS
.
Method
The procedure uses LSVECTORS
to obtain the required eigenvector.
Action with RESTRICT
If the DATA
parameter is set to a list of factors, these must not be restricted.
See also
Commands for: Time series.
Example
CAPTION 'MC1PSTATIONARY examples'; STYLE=meta "Input as transition probability matrix" MATRIX [ROWS=2; COLUMNS=2; VALUES=.95,.05,.10,.90] m MC1PSTATIONARY m "Input as factor of states" CALCULATE u=1+INT(5*URAND(855438; 1000)) GROUP u; FACTOR=fu MC1PSTATIONARY [PRINT=transitions,pstationary] fu "Input as transition count matrix" VARIATE [VALUES=(1...5)] vmact; DECIMALS=0 MATRIX [ROWS=vmact; COLUMNS=vmact] mact[1,2] READ mact[1] 1362 26 2 62 1 33 31 9 64 7 7 13 7 35 4 31 74 49 355 16 0 11 3 12 6 : READ mact[2] 1048 19 7 56 4 21 27 17 77 17 10 17 21 53 25 41 69 64 467 52 4 30 15 43 29 : TEXT [VALUES=sit,stand,walk,graze,pace] aname MC1PSTATIONARY [PRINT=transitions,pstationary] mact[1,2]; STATES=aname;\ PSTATIONARY=pact[1,2] PRINT pact[]