R: Mean First Passage Time for irreducible Markov chains

meanFirstPassageTime {markovchain} | R Documentation

## Mean First Passage Time for irreducible Markov chains

### Description

Given an irreducible (ergodic) markovchain object, this function calculates the expected number of steps to reach other states

### Usage

    meanFirstPassageTime(object, destination)

### Arguments

`object` | the markovchain object
`destination` | a character vector representing the states respect to which we want to compute the mean first passage time. Empty by default

### Details

For an ergodic Markov chain it computes:

- If destination is empty, the average first time (in steps) that takes the Markov chain to go from initial state i to j. (i, j) represents that value in case the Markov chain is given row-wise, (j, i) in case it is given col-wise.

- If destination is not empty, the average time it takes us from the remaining states to reach the states in `destination`

### Value

a Matrix of the same size with the average first passage times if destination is empty, a vector if destination is not

### Author(s)

Toni Giorgino, Ignacio Cordón

### References

C. M. Grinstead and J. L. Snell. Introduction to Probability. American Mathematical Soc., 2012.

### Examples

    m <- matrix(1 / 10 * c(6,3,1,
                           2,3,5,
                           4,1,5), ncol = 3, byrow = TRUE)
    mc <- new("markovchain", states = c("s","c","r"), transitionMatrix = m)
    meanFirstPassageTime(mc, "r")

    # Grinstead and Snell's "Oz weather" worked out example
    mOz <- matrix(c(2,1,1,
                    2,0,2,
                    1,1,2)/4, ncol = 3, byrow = TRUE)

    mcOz <- new("markovchain", states = c("s", "c", "r"), transitionMatrix = mOz)
    meanFirstPassageTime(mcOz)

[Package markovchain version 0.8.6 Index]