mfpt: Mean First Passage Times

In spdyn: Exploratory Space-Time Data Analysis

Mean First Passage Times

Description

Computes mean first passage times among states for a first order Markov process.

Usage

mfpt(M, tol = 1e-10)

Arguments

M	An object of class markov or class spMarkov.
tol	A tolerance argument, used in determining the steady state distribution. By default set to 1e-100.

Details

The mean first passage times matrix is estimated following the standard expression as found in Meyer (1978, p. 41). The mean first passage time refers to the time-steps it takes to reach state Si for the first time, given the initial state Sj.

Value

If an object of class markov is provided, it returns a vector. If an object of class spMarkov is provided, it returns a matrix.

Author(s)

Osmar Leandro Loaiza Quintero

References

Meyer, Carl (1978). 'An Alternative Expression for the Mean First Passage Matrix', Linear Algebra and its Applications, Vol.22,pp.41-47.

See Also

spMarkov,markov

Examples

data(usinc)
stateVars<-names(usinc[,7:87])
stateNames<-c('Poor','Lower','Middle','Upper','Rich')

##Classic Markov Matrix
Mc<-markov(usinc, stateVars=stateVars,n.states=5,stateNames=stateNames)
mfpt(Mc)

##Spatial Markov Matrix
#Create a list of spatial weights
require(spdep)
lw<-nb2listw(poly2nb(usinc,queen=TRUE),style='W')

Msp<-spMarkov(usinc, lw, stateVars=stateVars,
n.states=5,stateNames=stateNames,
pool=TRUE,std=TRUE)

mfpt(Msp)

spdyn documentation built on Oct. 28, 2024, 3 p.m.