IPPPinterval {IPPP}

Simulate the Number of Events in an Interval

Description

Generates random numbers that correspond to the number of events of an inhomogeneous Poisson point process (IPPP) in a given interval.

The IPPP is described by a rate function r.

Usage

IPPPinterval(from, to, xrate, yrate, no = 1, expsamplesize = NULL)

Arguments

from

Real number, describing the lower boundary of the interval of interest

to

Real number larger than from, describing the upper boundary of the interval of interest

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)

no

OPTIONAL, default is 1. The number of times the random number is determined

expsamplesize

OPTIONAL, default is NULL. Setting this parameter to a numeric value changes the average number of events generated by the IPPP as a whole to the chosen value. The number of events in the interval changes accordingly

Details

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

Value

Vector of length no, whose i-th entry contains the number of events in the interval generated in the i-th run.

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

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

Examples

#determine 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') 
#determine no of events between 3 and 6
from=3
to=5
lines(c(from,from),c(0,10)) #mark interval in the plot
lines(c(to,to),c(0,10))
#simulate the number of events in the interval [from, to]
IPPPinterval(from,to,xrate,yrate) #simulate the number of events in the interval [from, to]
#rescale so that the whole rate function will on average generate 200 events:
IPPPinterval(from,to,xrate,yrate,expsamplesize=200)
#now more events occur in the interval [from, to]!
#Make 20 repetitions of the upper simulation
IPPPinterval(from,to,xrate,yrate,no=20,expsamplesize=200)