Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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

`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 |

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

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

Niklas Hohmann

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)
``` |

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