IPPPcond {IPPP}

Simulate Location of Events for a Fixed Number of Events

Description

Returns a vector of random numbers that correspond to the location of events of an inhomogeneous Poisson point process (IPPP) in the case that the number of events is fixed.

The IPPP is described by a rate function r.

Usage

IPPPcond(samplesize, xrate, yrate, rnpr = 100)

Arguments

samplesize

Natural number. The number of events occurring

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)

rnpr

OPTIONAL, default is 100. The number of random numbers used per run in the loop of the rejection method. For 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 length samplesize, containing the locations of the simulated events

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 the unconditioned version with a random 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')
#simulate location of 5 events:
samplesize=5
p5=IPPPcond(samplesize,xrate,yrate) 
points(p5,rep(0,samplesize),cex=2) #plot results
#simulate location of 30 events
samplesize=30
p30=IPPPcond(samplesize,xrate,yrate) 
points(p30,rep(1,samplesize),cex=2,pch=3) #compare with former results