RHawkes (version 1.0)

simRHawkes: 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

simRHawkes(re.dist = rweibull, par.redist = list(shape = 1, scale = 1), 
           ofspr.den = function(x, p.ofd) 1 / p.ofd * exp(-x / p.ofd), 
           p.ofd = 1, branching.ratio = 0.5, cens = 1, B = 10, B0 = 50, 
           max.ofspr.den = max(optimize(ofspr.den, c(0, cens), maximum = TRUE, 
           p = p.ofd)$obj, ofspr.den(0, p.ofd), ofspr.den(cens, p.ofd)) * 1.1)

Arguments

re.dist

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

par.redist

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

ofspr.den

A (vectorized) function. The offspring density function.

p.ofd

A numeric vector. The parameters of the offspring density.

branching.ratio

A scalar. 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.

max.ofspr.den

A scalar. The maximum value of the offspring density function from 0 to cens.

Value

A numeric vector of all pooled events (immigration/birth) times of all generations 0, 1, ...

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.

Examples

# NOT RUN {
B <- 10; i <- 0;
tms <- replicate(B,
                  {cat(i<<-i+1,'\n');
                  simRHawkes(par.redist = list(shape = 3, scale = 1),
                      p.ofd = 0.5, branching.ratio = 0.5,
                      cens = 100)
                  })
# }