dmc_irreclass: Finding irreducible classes for discrete-time finite...

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

Description

dmc_irreclass focuses on irreducible classes for a given finite discrete-time Markov chain. This function tells you how many irreducible classes in this M.C. and included states of each class and it can also identify whether classes are closed and period of each class.

Usage

dmc_irreclass(MC, period = TRUE, whetherc = TRUE, r_or_t = TRUE)

Arguments

MC	is an object in class 'stat2003.d'
period	A logical scalar. If TRUE (the default) dmc_irreclass will also returns the period of each class.
whetherc	A logical scalar. If TRUE (the default) dmc_irreclass will also identifies whether classes are closed.
r_or_t	A logical scalar. If TRUE (the default) dmc_irreclass will also identifies whether classes are (positive) recurrent or transient

Value

dmc_irreclass returns a table about all irreducible classes.

See Also

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

dmc_equi returns the equilibrium distribution for a discrete-time Markov chain.

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_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), nr = 4, nc=4, byrow = TRUE)
A <- new("stat2003.d", p_start = c(1/2, 0, 0, 1/2), p = m,
         statespace = c("0", "1", "C", "D") )

dmc_irreclass(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), nr = 5, nc=5, byrow = TRUE)

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

dmc_irreclass(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), nr = 7, nc=7, byrow = TRUE)

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

dmc_irreclass(A)

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