dmc_equi: Equilibrium distribution of a discrete-time finite statespace...

In paulnorthrop/stat2003: stat2003: Introduction to Applied Probability at UCL

Description

dmc_equi is used to find the equilibrium distribution of a discrete-time finite statespace Markov chain.

Usage

dmc_equi(MC)

Arguments

MC	is an object in class 'stat2003.d'

Value

dmc_equi will return a vector if the Marchov chain has equilibrium distribution.

See Also

stat2003.d-class A class type of discrete-time finite state space Markov chain in stat2003 package.

dmc_inv returns the invariant distribution for a discrete-time Markov chain.

dmc_simu simulates a discrete-time Markov chain by returning one possible sequence and a states against steps plot.

dmc_tp can calculate transient probabilities at a specific step, and also can give a graph about transient probabilities from step zero to that specific step.

dmc_irreclass focuses on irreducible classes for a given discrete-time Markov chain

dmc_period returns the period of each state for a given discrete-time Markov chain

Examples

m <- matrix(c(0, 1, 0, 0,
             1, 0, 0, 0,
             1/4, 1/4, 1/4,1/4,
             0, 0, 1, 0), nrow = 4, ncol=4, byrow = TRUE)

A <- new("stat2003.d", p_start = c(1/2, 0, 0, 1/2), p = m,
          statespace = letters[1 : 4] )

dmc_equi(A)



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

A <- new("stat2003.d", p_start = c(0, 0, 0, 1, 0), p = m,
         statespace = c("1", "2", "C", "4", "E") )

dmc_equi(A)


m <- matrix(c(0, 1, 0, 0, 0, 0, 0,
              0, 0, 1, 0, 0, 0, 0,
              0, 1/3, 0, 2/3, 0, 0, 0,
              0, 0, 0, 0, 2/3, 1/3, 0,
              0, 2/3, 0, 1/3, 0, 0, 0,
              0, 0, 0, 0, 0, 1/3, 2/3,
              0, 0, 0, 0, 0, 1/4, 3/4), nrow = 7, ncol=7, byrow = TRUE)

A <- new("stat2003.d", p_start = c(0, 0, 0, 1, 0, 0, 0), p = m,
        statespace = LETTERS[1 : 7] )

dmc_equi(A)


m <- matrix(c(1, 0, 0, 0, 0, 0,
              1/4, 0, 3/4, 0, 0, 0,
              0, 1/2, 0, 1/2, 0, 0,
              0, 0, 1/2, 0, 1/3, 1/6,
              0, 0, 0, 0, 1/4, 3/4,
              0, 0, 0, 0, 1/3, 2/3), nrow = 6, ncol=6, byrow = TRUE)
A <- new("stat2003.d", p_start = c(0, 0, 0, 1, 0, 0), p = m,
        statespace = c("1", "2", "3", "4", "5", "6") )

dmc_equi(A)

paulnorthrop/stat2003 documentation built on May 24, 2019, 10:31 p.m.