Non-homogeneous discrete time Markov chain class

The S4 class of non-homogeneous discrete time Markov chains: a sequence of markovchain objects, the \(k\)-th giving the transition probabilities from time \(k - 1\) to time \(k\).

Slots

markovchains: A list of markovchain objects.
name: Optional name of the object.

Note

The class consists in a list of markovchain objects. It is aimed at working with non homogeneous Markov chains.

Objects from the Class

Objects are created with new("markovchainList", markovchains = list(...)) or estimated by markovchainListFit(). The transition probabilities, and the states, may change from one time to the next.

Methods

[[: signature(x = "markovchainList"): extract the i-th markovchain
dim: signature(x = "markovchainList"): number of markovchain underlying the matrix
predict: signature(object = "markovchainList"): predict from a markovchainList
print: signature(x = "markovchainList"): prints the list of markovchains
show: signature(object = "markovchainList"): same as print

References

A First Course in Probability (8th Edition), Sheldon Ross, Prentice Hall 2010

Author

Giorgio Spedicato

Examples

showClass("markovchainList")
#> Class "markovchainList" [package "markovchain"]
#> 
#> Slots:
#>                                 
#> Name:  markovchains         name
#> Class:         list    character
#define a markovchainList
statesNames=c("a","b")

mcA<-new("markovchain",name="MCA", 
         transitionMatrix=matrix(c(0.7,0.3,0.1,0.9),
                          byrow=TRUE, nrow=2, 
                          dimnames=list(statesNames,statesNames))
        )
                                                           
mcB<-new("markovchain", states=c("a","b","c"), name="MCB",
         transitionMatrix=matrix(c(0.2,0.5,0.3,0,1,0,0.1,0.8,0.1),
         nrow=3, byrow=TRUE))
 
mcC<-new("markovchain", states=c("a","b","c","d"), name="MCC",
         transitionMatrix=matrix(c(0.25,0.75,0,0,0.4,0.6,
                                   0,0,0,0,0.1,0.9,0,0,0.7,0.3), 
                                 nrow=4, byrow=TRUE)
)
mcList<-new("markovchainList",markovchains=list(mcA, mcB, mcC), 
           name="Non - homogeneous Markov Chain")