Description Usage Arguments Details Value References See Also Examples
This function estimates the Ffunction in a set of homogenous or nonhomogeneous point processes, D. The Ffunction is evaluated in a grid of values r, and it can be optionally plotted.
It calls the auxiliary functions NHFaux and other functions not intended for users.
1 2 
lambdaD 
A matrix of positive values. Each column is the intensity vector of one of the point process in D. If there is only one process in D, it can be a vector or even a numeric value if the process is homogeneous. 
T 
Numeric value. Length of the observed period. It only must be specified
if the number of rows in 
Ptype 
Optional. Label: "hom" or "inhom". The first one indicates that all the point processes in sets C and D are homogeneous. 
posD 
Numeric vector. Occurrence times of the points in all the point processes in D. 
typeD 
Numeric vector with the same length as 
r 
Numeric vector. Values where the Ffunction must be evaluated. If it is NULL, a default vector is used, see Details 
L 
Optional. Numeric vector. Values in the observed period used to calculate the Ffunction. If it is NULL, a default vector is used, see Details. 
dplot 
Optional. Logical flag. If it is true, the Ffunction is plotted. 
tit 
Optional. The title to be used in the plot of the Ffunction. 
... 
Further arguments to be passed to the function 
The information about the processes is provided by arguments posD
, the vector of all the occurrence times
in the processes in C, and typeD
, the vector of the code of the point process in set D
where each point in posD
has occurred.
This function estimates the Ffunction in a set D of homogenous or nonhomogeneous time point processes, see Cebrian et al (2020) for details of the estimation. The Ffunction, also known as empty space function, is the distribution function of the distances from an arbitray point in the space to the nearest point in a process in D. In homogeneous processes, it estimates the probability that at least one point in processes in D occurs at a distance lower than r of an arbitray point in the space. If the processes are nonhomogenous, the inhomogenous version of the function, adjusted for time varying intensities, is used.
If argument r
is NULL, the following grid is used to evaluate the function
r1<max(20, floor(T/20))
r<seq(1,r1,by=2)
if (length(r)>200) r<seq(1,r1,length.out=200)
If argument L
is NULL, the following grid is used
L < seq(1, T, by = 2) if (length(L) > 5000) L < seq(1, T, by = round((T  1)/199))
A list with elements:
r 
Vector of values r where the Ffunction is estimated. 
NHFr 
Estimated values of F_{D}(r). 
T 
Length of the observed period of the process. 
L 
Grid of L values to calculate the Ffuntion. 
Cebrian, A.C., Abaurrea, J. and Asin, J. (2020). Testing independence between two point processes in time. Journal of Simulation and Computational Statistics.
1 2 3 4 5 6 7 8 9 10 11 12 13  set.seed(123)
lambda1<runif(500, 0.05, 0.1)
pos1<simNHPc(lambda=lambda1, fixed.seed=123)$posNH
aux<NHF(lambdaD=lambda1, posD=pos1, typeD=1)
aux$NHFr
#Set D with two processes ***
#lambda2<runif(1000, 0.01, 0.2)
#pos2<simNHPc(lambda=lambda2, fixed.seed=123)$posNH
#aux<NHF(lambdaD=cbind(lambda1,lambda2), posD=c(pos1,pos2),
# typeD=c(rep(1, length(pos1)), rep(2, length(pos2))) )
#aux$NHFr

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