compdelta {HiddenMarkov}R Documentation

Marginal Distribution of Stationary Markov Chain

Description

Computes the marginal distribution of a stationary Markov chain with transition probability matrix Π\Pi. The mm discrete states of the Markov chain are denoted by 1,,m1, \cdots, m.

Usage

compdelta(Pi)

Arguments

Pi

is the m×mm \times m transition probability matrix of the Markov chain.

Details

If the Markov chain is stationary, then the marginal distribution δ\delta satisfies

δ=δΠ. \delta = \delta \Pi \,.

Obviously,

jmδj=1. \sum_j^m \delta_j = 1.

Value

A numeric vector of length mm containing the marginal probabilities.

Examples

Pi <- matrix(c(1/2, 1/2,   0,   0,   0,
               1/3, 1/3, 1/3,   0,   0,
                 0, 1/3, 1/3, 1/3,   0,
                 0,   0, 1/3, 1/3, 1/3,
                 0,   0,   0, 1/2, 1/2),
             byrow=TRUE, nrow=5)

print(compdelta(Pi))

[Package HiddenMarkov version 1.8-13 Index]