HiddenMarkov (version 1.8-14)

compdelta: Marginal Distribution of Stationary Markov Chain

Description

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

Usage

compdelta(Pi)

Value

A numeric vector of length \(m\) containing the marginal probabilities.

Arguments

Pi

is the \(m \times m\) transition probability matrix of the Markov chain.

Details

If the Markov chain is stationary, then the marginal distribution \(\delta\) satisfies $$ \delta = \delta \Pi \,. $$ Obviously, $$ \sum_j^m \delta_j = 1. $$

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))