mapfit (version 0.9.9)

map.mmoment: Moments for Markovian arrival pcess (MAP)

Description

Moments for MAP.

Usage

map.mmoment(k, map)
map.jmoment(lag, map)
map.acf(map)

Arguments

k

An integer of dgrees of moments.

map

An object of S4 class of MAP ('>map, '>gmmpp).

lag

An integer of time lag for corrleation.

Value

map.mmoment gives a vector of up to k moments. map.jmoment gives a matrix of \(s_{ij}(lag), i=1,..,n, j=1,..,n\) where n is the size of phases. map.acf gives a vector of up to n-lag correlation, where n is the size of phases.

Details

MAP parameters are \(\alpha\), \(D_0\) and \(D_1\); $$P = (-D_0)^{-1} D_1$$ and $$s P = s.$$

Then the moments for MAP are marginal moment; $$m_k = k! s (-D_0)^{-k} 1,$$ joint moment; $$s_{ij}(lag) = i! j! s (-D_0)^{-i} P^{lag} (-D_0)^{-j} 1,$$ k-lag correlation (autocorrelation); $$rho(lag) = (s_{11}(lag) - m_1^2)/(m_2 - m_1^2)$$

See Also

map, gmmpp, erhmm

Examples

# NOT RUN {
## create an MAP with specific parameters
(param1 <- map(alpha=c(1,0,0),
               D0=rbind(c(-4,2,0),c(2,-5,1),c(1,0,-4)),
               D1=rbind(c(1,1,0),c(1,0,1),c(2,0,1))))

## create an ER-HMM with specific parameters
(param2 <- erhmm(shape=c(2,3), alpha=c(0.3,0.7),
                 rate=c(1.0,10.0),
                 P=rbind(c(0.3, 0.7), c(0.1, 0.9))))

## marginal moments of MAP
map.mmoment(k=3, map=param1)
map.mmoment(k=3, map=as(param2, "map"))

## joint moments of MAP
map.jmoment(lag=1, map=param1)
map.jmoment(lag=1, map=as(param2, "map"))

## k-lag correlation
map.acf(map=param1)
map.acf(map=as(param2, "map"))

# }