simHawkes1a: Simulate an (inhomogeneous) Hawkes self-exciting process `simHawkes1a` simulates the event times of an inhomogeneous Hawkes process (IHSEP) with background event intensity/rate $nu(\cdot)\geq 0$, branching ratio $\eta\in[0,1)$, and offspring birthtime density $g(\cdot)$, up to a censoring time $T$.

Description

Simulate an (inhomogeneous) Hawkes self-exciting process simHawkes1a simulates the event times of an inhomogeneous Hawkes process (IHSEP) with background event intensity/rate $nu(\cdot)\geq 0$, branching ratio $\eta\in[0,1)$, and offspring birthtime density $g(\cdot)$, up to a censoring time $T$.

Usage

simHawkes1a(
  nu = function(x) rep(100, length(x)),
  cens = 1,
  nuM = max(optimize(nu, c(0, cens), maximum = TRUE)$obj, nu(0), nu(cens),
    .Machine$double.eps^0.5) * 1.1,
  br = 0.5,
  dis = "exp",
  par.dis = list(rate = 1)
)

Value

a vector giving the event times of an inhomogeneous Hawkes process up to the censoring time in ascending order.

Arguments

nu: a function, which gives the background event intensity function $\nu(\cdot)$; needs to be a bounded function on $[0,T]$.
cens,: a positive scalar, which gives the censoring time.
nuM,: positive scalar, optional argument giving the maximum of the background intensity function on $[0,T]$.
br,: scalar in [0,1), giving the branching ratio.
dis,: character string giving the name of the child birthtime distribution; 'd$dis' gives the density function $g(\cdot)$.
par.dis,: a (named) list giving the values of the parameters of the child birthtime distribution.