compdelta {HiddenMarkov}

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.

Details

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

\delta = \delta \Pi \,.

Obviously,

\sum_j^m \delta_j = 1.

Value

A numeric vector of length m 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))