HiddenMarkov (version 1.8-13)

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)

Arguments

Pi

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

Value

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

Details

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

Examples

# NOT RUN {
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))
# }