sim.pred {RHawkes}

Simulate a fitted RHawkes process model

Description

Simulate a fitted RHawkes process model after the censoring time cens to a future time point cens.tilde.

Usage

sim.pred(tms, re.dist = rweibull, par, 
    par.redist = list(shape = par[1], scale = par[2]), 
    h.fn = function(x, p) dexp(x, rate = 1 / p), p.ofd = par[3], 
    branching.ratio = par[4], cens, cens.tilde = cens * 1.5, 
    mu.fn = function(x, p) {
        exp(dweibull(x, shape = p[1], scale = p[2], log = TRUE) - 
        pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, log.p = TRUE))
    })

Arguments

tms

A numeric vector, with values sorted in ascending order. Event times to fit the RHawkes point process model.

re.dist

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

par

A numeric vector, giving the parameters of the model with the immigration parameters \mu(.), offspring parameters h(.) and lastly the branching ratio \eta(.).

par.redist

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

h.fn

A (vectorized) function. The offspring density function.

p.ofd

A (named) list. The parameters of the offspring density.

branching.ratio

A scalar. The branching ratio parameter.

cens

A scalar. The censoring time.

cens.tilde

A scalar. The future time that the simulation run until.

mu.fn

A (vectorized) function. The immigration hazard function.

Value

A numeric vector that contains the simulated event times from censoring time cens up until cens.tilde

Author(s)

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

Examples

N <- 5; i <- 0;
data(quake); tms <- sort(quake$time);
# add some random noise the simultaneous occurring event times
tms[213:214] <- tms[213:214] + 
                    sort(c(runif(1, -1, 1)/(24*60), runif(1, -1, 1)/(24*60)))
# simulate future event time based on MLE fitted RHawkes model
times <- replicate(N,
                   {cat(i<<-i+1,'\n');
                   sim.pred(tms = tms, par = c(0.314, 22.2, 1266, 0.512),
                            cens=35063)
                   })
plot(NA,NA,xlim=c(0,35063*1.5),ylim=c(0,max(lengths(times))+nrow(quake)),
     xlab="time",ylab="Sample path")
lines(c(0,quake$time),0:nrow(quake),type="s")
for(i in 1:N)
    lines(c(tail(quake$time,1),times[[i]]),nrow(quake)+0:length(times[[i]]),
          type="s",lty=2)