giddy.ergodic.steady_state¶

giddy.ergodic.steady_state(P)[source]¶

Calculates the steady state probability vector for a regular Markov transition matrix P.

Parameters

Parray: (k, k), an ergodic Markov transition probability matrix.

Returns

: array: (k, ), steady state distribution.

Examples

Taken from [KS67]. Land of Oz example where the states are Rain, Nice and Snow, so there is 25 percent chance that if it rained in Oz today, it will snow tomorrow, while if it snowed today in Oz there is a 50 percent chance of snow again tomorrow and a 25 percent chance of a nice day (nice, like when the witch with the monkeys is melting).

>>> import numpy as np
>>> from giddy.ergodic import steady_state
>>> p=np.array([[.5, .25, .25],[.5,0,.5],[.25,.25,.5]])
>>> steady_state(p)
array([0.4, 0.2, 0.4])

Thus, the long run distribution for Oz is to have 40 percent of the days classified as Rain, 20 percent as Nice, and 40 percent as Snow (states are mutually exclusive).