markovchain (version 0.4.4)

absorbingStates: Various function to perform structural analysis of DTMC

Description

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

Usage

absorbingStates(object)
transientStates(object)
canonicForm(object)
communicatingClasses(object)
recurrentClasses(object)
period(object)

Arguments

object

A markovchain object.

Value

• A matrix

References

Feres, Matlab listing for markov chain.

See Also

markovchain

Examples

statesNames=c("a","b","c")
markovB<-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)
                 ))
absorbingStates(markovB)
transientStates(markovB)
communicatingClasses(markovB)
canonicForm(markovB)
#periodicity analysis
E=matrix(0,nrow=4,ncol=4)
E[1,2]=1
#E[2,c(1, 3)]=1/2;
E[2,1]=1/3;E[2,3]=2/3
#E[3,c(2, 4)]=1/2;
E[3,2]=1/4;E[3,4]=3/4
E[4,3]=1
mcE <- new("markovchain", states = c("a", "b", "c", "d"), 
                 transitionMatrix = E, 
                 name = "E")

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

myMatr<-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)
myMc<-new("markovchain",transitionMatrix=myMatr)
period(myMc)