IPPPuncond {IPPP}

Simulate Events according to an Inhomogeneous Poisson Point Process

Description

Generates random numbers corresponding to the locations of events of an inhomogeneous Poisson point process (IPPP). The IPPP is described by a rate function r.

Usage

IPPPuncond(xrate, yrate, expsamplesize = NULL, rnpr = 100)

Arguments

xrate

Vector of (strictly increasing) real numbers

yrate

Vector of positive real numbers of the same length as xrate. The vectors xrate and yrate form the rate function r in the sense that r=approxfun(xrate,yrate)

expsamplesize

OPTIONAL, default is NULL. If this variable is set to a numeric value, it determines the average number of events occurring

rnpr

OPTIONAL, default is 100. The number of random numbers used per run in the loop of the rejection method. For more details see the corresponding preprint

Details

Below min(xrate) and above max(xrate), the rate function r is assumed to have the value zero.

Value

A vector of variable length, containing the generated locations of the events. If no events occur, the output is numeric(0)

Author(s)

Niklas Hohmann

References

Hohmann, Niklas. "Conditional Densities and Simulations of Inhomogeneous Poisson Point Processes: The R package "IPPP"" arXiv 2019. <arXiv:1901.10754>

See Also

IPPPuncond for a version with a fixed number of events occurring.

vignette("IPPP") for an overview of the features of the IPPP package and some background.

Examples

#Define rate function
sx=1:5
sy=c(0,1,1,3,0)
sm=c(1,0,1,0,-1)
xrate=seq(1,5,length.out=100)
yrate=splinefunH(sx,sy,sm)(xrate)
#plot rate function
plot(xrate,yrate,type='l',xlim=c(0.5,5.5), main='Rate Function') 

p=IPPPuncond(xrate,yrate) #simulate one set of events
points(p,rep(0,length(p)),cex=2) #plot results
#simulate location of events with the expected number of events being 20
expsamplesize=20
pp=IPPPuncond(xrate,yrate,expsamplesize) 
length(pp) #in most cases, the result is not exactely 20
points(pp,rep(1,length(pp)),cex=2,pch=3) #compare with former results