A class to handle non - homogeneous Markov chains

A `markovchainlist`

is a list of `markovchain`

objects. They can be used to model non - homogeneous discrete time Markov Chains, when transition probabilities (and possible states) change by time.

`markovchains`

:Object of class

`"list"`

: a list of markovchains`name`

:Object of class

`"character"`

: optional name of the class

- [[
`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`

`signature(x = "markovchainList")`

: prints the list of markovchains- show
`signature(object = "markovchainList")`

: same as`print`

The class consists in a list of `markovchain`

objects.
It can help to deal with non - homogeneous Markov chains.

Giorgio Spedicato

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

`markovchain`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
showClass("markovchainList")
#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")
``` |

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