IPPPinterval: Simulate the Number of Events in an Interval In IPPP: Inhomogeneous Poisson Point Processes

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

 `1` ```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.

Niklas Hohmann

References

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

`vignette("IPPP")` for an overview of the features of the IPPP package and some background.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```#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) ```