statdistr: Computing Stationary Distribution

In DTMCPack: Suite of Functions Related to Discrete-Time Discrete-State Markov Chains

Computing Stationary Distribution

Description

This function computes the stationary distribution of a markov chain (assuming one exists) using the formula from proposition 2.14.1 of Resnick: pi=(1,...1)(I-P+ONE)^(-1), where I is an mxm identity matrix, P is an mxm transition matrix, and ONE is an mxm matrix whose entries are all 1. This formula works well if the number of states is small, but since it directly computes the inverse of the matrix, it is not tractable for larger matrices. For larger matrices 1/E(FPTime(n)) is a rough approximation for the long run proportion of time spent in a state n.

Usage

statdistr(tmat)

Arguments

tmat	Markov chain transition matrix, must be a square matrix and rows must sum to 1.

Value

Returns a stationary distribution: mxm matrix which represents the long run percentage of time spent in each state.

Author(s)

Will Nicholson

References

Resnick, "Adventures in Stochastic Processes"

Examples

data(hh)
statdistr(hh)

DTMCPack documentation built on April 11, 2022, 9:05 a.m.