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

View source: R/IPPPnthpointdens.R

Determines values of the probability density function of the n-th point of an inhomogeneous Poisson point process (IPPP), given that a fixed number of events occur. The IPPP is described by a rate function r.

1 | ```
IPPPnthpointdens(x, n, samplesize, xrate, yrate)
``` |

`x` |
Vector of real numbers where the value of the probability density is determined |

`n` |
Natural number smaller than samplesize. Determines the event for which the probability density is determined. 1=first event from the left, i=i-th event from the left. |

`samplesize` |
Natural number. The overall 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) |

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

A list containing two entries:

` x ` |
A duplicate of the input of the same name |

` densval ` |
A vector consisting of the values of the probability density, evaluated at x |

Niklas Hohmann

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

`IPPPconddens`

for the probability density of the n-th event above/below the location of some given event.

`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 | ```
sx=c(1,2,3,4,5)
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')
x=seq(0,6,length.out = 1000) #point where the pdf is determined
n=1 #get the pdf of the first point from the left ...
samplesize=5 #... out of a sample of five
ll=IPPPnthpointdens(x,n,samplesize,xrate,yrate)
plot(ll$x,ll$densval,type='l') #plot the resulting pdf
legend('topleft',legend=paste('pdf of point no.',as.character(n),
'out of ',as.character(samplesize)), 'points' ,lty=1)
``` |

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