structuralAnalysis: Various function to perform structural analysis of DTMC
In markovchain: Easy Handling Discrete Time Markov Chains

period

R Documentation

Various function to perform structural analysis of DTMC

Description

These functions return absorbing and transient states of the markovchain objects.

Usage

period(object)

communicatingClasses(object)

recurrentClasses(object)

transientClasses(object)

transientStates(object)

recurrentStates(object)

absorbingStates(object)

canonicForm(object)

Arguments

object

A markovchain object.

Value

period: returns a integer number corresponding to the periodicity of the Markov chain (if it is irreducible)
absorbingStates: returns a character vector with the names of the absorbing states in the Markov chain
communicatingClasses: returns a list in which each slot contains the names of the states that are in that communicating class
recurrentClasses: analogously to communicatingClasses, but with recurrent classes
transientClasses: analogously to communicatingClasses, but with transient classes
transientStates: returns a character vector with all the transient states for the Markov chain
recurrentStates: returns a character vector with all the recurrent states for the Markov chain
canonicForm: returns the Markov chain reordered by a permutation of states so that we have blocks submatrices for each of the recurrent classes and a collection of rows in the end for the transient states

Author(s)

Giorgio Alfredo Spedicato, Ignacio Cordón

References

Feres, Matlab listing for markov chain.

Examples

statesNames <- c("a", "b", "c")
mc <- new("markovchain", states = statesNames, transitionMatrix =
          matrix(c(0.2, 0.5, 0.3,
                   0,   1,   0,
                   0.1, 0.8, 0.1), nrow = 3, byrow = TRUE,
                 dimnames = list(statesNames, statesNames))
         )

communicatingClasses(mc)
recurrentClasses(mc)
recurrentClasses(mc)
absorbingStates(mc)
transientStates(mc)
recurrentStates(mc)
canonicForm(mc)

# periodicity analysis
A <- matrix(c(0, 1, 0, 0, 0.5, 0, 0.5, 0, 0, 0.5, 0, 0.5, 0, 0, 1, 0), 
            nrow = 4, ncol = 4, byrow = TRUE)
mcA <- new("markovchain", states = c("a", "b", "c", "d"), 
          transitionMatrix = A,
          name = "A")

is.irreducible(mcA) #true
period(mcA) #2

# periodicity analysis
B <- matrix(c(0, 0, 1/2, 1/4, 1/4, 0, 0,
                   0, 0, 1/3, 0, 2/3, 0, 0,
                   0, 0, 0, 0, 0, 1/3, 2/3,
                   0, 0, 0, 0, 0, 1/2, 1/2,
                   0, 0, 0, 0, 0, 3/4, 1/4,
                   1/2, 1/2, 0, 0, 0, 0, 0,
                   1/4, 3/4, 0, 0, 0, 0, 0), byrow = TRUE, ncol = 7)
mcB <- new("markovchain", transitionMatrix = B)
period(mcB)

markovchain documentation built on Sept. 24, 2023, 5:06 p.m.