# IPPPuncond: Simulate Events according to an Inhomogeneous Poisson Point... In IPPP: Inhomogeneous Poisson Point Processes

## 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

 `1` ```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)

Niklas Hohmann

## References

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

`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.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```#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 ```