| stationary_p {LaMa} | R Documentation |
Compute the periodically stationary distribution of a periodically inhomogeneous Markov chain
Description
If the transition probability matrix of an inhomogeneous Markov chain varies only periodically (with period length L), it converges to a so-called periodically stationary distribution.
This happens, because the thinned Markov chain, which has a full cycle as each time step, has homogeneous transition probability matrix
\Gamma_t = \Gamma^{(t)} \Gamma^{(t+1)} \dots \Gamma^{(t+L-1)} for all t = 1, \dots, L.
The stationary distribution for time t satifies \delta^{(t)} \Gamma_t = \delta^{(t)}.
This function calculates the periodically stationary distribution.
Usage
stationary_p(Gamma, t = NULL, tol = .Machine$double.eps)
Arguments
Gamma |
Array of transition probability matrices of dimension c(N,N,L). |
t |
Integer index of the time point in the cycle, for which to calculate the stationary distribution If t is not provided, the function calculates all stationary distributions for each time point in the cycle. |
tol |
The tolerance for detecting linear dependencies in the columns of the thinned transition matrix. The default is .Machine$double.eps. |
Value
Either the periodically stationary distribution at time t or all periodically stationary distributions.
Examples
L = 24
beta = matrix(c(-1, 2, -1, -2, 1, -1), nrow = 2, byrow = TRUE)
Gamma = tpm_p(1:L, L, beta, degree = 1)
# Periodically stationary distribution for specific time point
delta = stationary_p(Gamma, 4)
# All periodically stationary distributions
Delta = stationary_p(Gamma)