giddy.ergodic.fmpt¶
-
giddy.ergodic.
fmpt
(P)[source]¶ Calculates the matrix of first mean passage times for an ergodic transition probability matrix.
- Parameters
- Parray
(k, k), an ergodic Markov transition probability matrix.
- Returns
- Marray
(k, k), elements are the expected value for the number of intervals required for a chain starting in state i to first enter state j. If i=j then this is the recurrence time.
Notes
Uses formulation (and examples on p. 218) in [KS67].
Examples
>>> import numpy as np >>> from giddy.ergodic import fmpt >>> p=np.array([[.5, .25, .25],[.5,0,.5],[.25,.25,.5]]) >>> fm=fmpt(p) >>> fm array([[2.5 , 4. , 3.33333333], [2.66666667, 5. , 2.66666667], [3.33333333, 4. , 2.5 ]])
Thus, if it is raining today in Oz we can expect a nice day to come along in another 4 days, on average, and snow to hit in 3.33 days. We can expect another rainy day in 2.5 days. If it is nice today in Oz, we would experience a change in the weather (either rain or snow) in 2.67 days from today. (That wicked witch can only die once so I reckon that is the ultimate absorbing state).