fitHigherOrderMarkovChain: Functions to fit a higher order Markov chain

Description Usage Arguments Value Note Author(s) References See Also Examples

Description

Given a sequence of states arising from a stationary state, it fits the underlying Markov chain distribution with higher order.

Usage

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Arguments

sequence

A character list.

order

Markov chain order

Value

A list containing lambda, Q, and X.

Note

This function is written in Rcpp.

Author(s)

Giorgio Spedicato, Tae Seung Kang

References

Ching, W. K., Huang, X., Ng, M. K., & Siu, T. K. (2013). Higher-order markov chains. In Markov Chains (pp. 141-176). Springer US.

Ching, W. K., Ng, M. K., & Fung, E. S. (2008). Higher-order multivariate Markov chains and their applications. Linear Algebra and its Applications, 428(2), 492-507.

package version 0.2.5

See Also

markovchain

Examples

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sequence<-c("a", "a", "b", "b", "a", "c", "b", "a", "b", "c", "a", "b", "c", "a"
            , "b", "c", "a", "b", "a", "b")
fitHigherOrder(sequence)

Example output

Package:  markovchain
Version:  0.6.9.3
Date:     2017-05-08
BugReport: http://github.com/spedygiorgio/markovchain/issues

$lambda
[1] 1.000000e+00 1.626307e-08

$Q
$Q[[1]]
      a         b    c
a 0.125 0.4285714 0.75
b 0.750 0.1428571 0.25
c 0.125 0.4285714 0.00

$Q[[2]]
          a         b    c
a 0.1428571 0.5714286 0.25
b 0.4285714 0.2857143 0.75
c 0.4285714 0.1428571 0.00


$X
  a   b   c 
0.4 0.4 0.2 

markovchain documentation built on Aug. 16, 2017, 5:11 p.m.