Gives the stationary probabilities for a 1st-order Markov chain (R.P. Littlejohn).

### Option

`PRINT` = string token |
What to print (`transitions` , `pstationary` ); default `psta` |
---|

### Parameters

DATA = matrices or factors |
Specifies the Markov chain as a factor, or matrix of transitions |
---|---|

`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[]