simRHawkes1 {RHawkes}

Simulate a renewal Hawkes (RHawkes) process

Description

Simulate a renewal Hawkes (RHawkes) process with given renewal immigration distribution function, offspring density function and branching ratio.

Usage

simRHawkes1(re.dist = rweibull, par.redist = list(shape = 1, scale = 1), 
            of.dis = "exp", par.ofdis = list(rate=1),
            branching.ratio = 0.5, cens = 1, B = 10, B0 = 50, 
            flatten=TRUE)

Arguments

re.dist

A (vectorized) function. The immigrant renewal distribution function.

par.redist

A numeric vector. The parameters of the immigrant renewal distribution.

of.dis

A character string indicating the distribution for the offspring birth times, which has to be the 'distname' part of the rdistname functions for simulating postive random variables implemented in R, such as "exp", "weibull", "gamma", "lnorm", etc.

par.ofdis

A list with named elements, giving the list of parameters of the offspring distribution, such as list(rate=1), list(shape=1,scale=1), etc.

branching.ratio

A scalar between 0 and 1, the branching ratio parameter.

cens

A scalar. The censoring time.

B

A scalar. Tuning parameter for simulation of further immigrants.

B0

A scalar. Tuning parameter for simulation of initial immigrants.

flatten

A boolean scalar, which indicates whether the output events times should be flattened into an increasing sequence of times, or not (in which case the output is the immigrant arrival times, and the offspring birth times for different immigrants).

Details

The function works by simulating the arrival times of immigrants according to the renewal immigration distribution. The birth times of offspring from each immigrant are then simulated according to an inhomogeneous Poisson processes with appropriate intensity functions.

Value

A numeric vector of pooled event (immigration/offspring birth) times of all generations 0, 1, ..., if flatten=TRUE; A list with two components: immitimes for immigrant arrival times, and offspringtimes for birth times of offspring due to different immigrants.

Author(s)

Feng Chen <[e-mail]> Tom Stindl <[e-mail]>

Examples

tms <- simRHawkes1(par.redist = list(shape = 3, scale = 1),
                   par.ofdis = list(rate=0.5), branching.ratio = 0.5,
                   cens = 50)
plot(stepfun(tms,0:length(tms)),do.points=FALSE,vertical=FALSE,xlim=c(0,50))

tms.clust <- simRHawkes1(par.redist = list(shape = 3, scale = 1),
                         par.ofdis = list(rate=0.5), branching.ratio = 0.5,
                         cens = 50,flatten=FALSE)
plot(c(0,50),c(0, 1+(nt <-length(it <- tms.clust$immitimes))),
     type="n",xlab="time",ylab="cluster")
segments(x0 = it,y0=-0.2,y1=0.2)
for(i in 1:nt)
    segments(x0 = c(it[i],it[i]+tms.clust$offspringtimes[[i]]),
             y0=i-0.2,y1=i+0.2)
abline(h=0:(nt+1),col="light gray",lty=2)
segments(x0=unlist(lapply(1:nt,function(i)c(it[i],it[i]+tms.clust$offspringtimes[[i]]))),
         y0=nt+1-0.2,y1=nt+1+0.2)