Description Usage Arguments Details Value References See Also Examples
This function estimates the cross nearest neighbour distance distribution function, D, between two sets, C and D, of (homogenous or nonhomogeneous) point processes. The Dfunction is evaluated in a grid of values r, and it can be optionally plotted.
It calls the auxiliary functions NHDaux and other functions, not intended for users.
1 2 
lambdaC 
A matrix of positive values. Each column is the intensity vector of one of the point processes in C. If there is only one process in C, it can be a vector or even a numeric value if the process is homogeneous. 
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. 
posC 
Numeric vector. Occurrence times of the points in all the point processes in C. 
typeC 
Numeric vector with the same length as 
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 Dfunction must be evaluated. If it is NULL, a default vector is used, see Details. 
dplot 
Optional. A logical flag. If it is TRUE, the Dfunction is plotted. 
tit 
Optional. The title to be used in the plot of the Dfunction. 
... 
Further arguments to be passed to the function 
The information about the processes is provided by arguments posC
, the vector of all the occurrence times
in the processes in C, and typeC
, the vector of the code of the point process in set C where each point in posC
has occurred;
the second set D is characterized analogously by typeD
and posD
.
This function estimates the Dfunction between two sets, C and D, of (homogenous or nonhomogeneous) point processes, see Cebrian et al (2020) for details of the estimation. The Dfunction is the distribution function of the distances from a point in a process in C to the nearest point in a process D. In homogeneous proceesses, it estimates the probability that at least one point in a process in set D occurs at a distance lower than r of a given point in a process in set C. If the processes are nonhomogenous, the inhomogenous version of the function, adjusted for time varying intensities, is used. It is calculated using the Hanisch estimator, see Van Lieshout (2006) Small values of the Dfunction suggest few points in processes in D in the rneighbourhood of points of processes in C. Large values indicate that points in processes in D are attracted by those of processes in C.
For inference about independence of the processes, K and Jfunctions should be 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)
A list with elements:
r 
Vector of values r where the Dfunction is estimated. 
NHDr 
Estimated values of D_{CD}(r). 
T 
Length of the observed period. 
Cebrian, A.C., Abaurrea, J. and Asin, J. (2020). Testing independence between two point processes in time. Journal of Simulation and Computational Statistics.
Van Lieshout, M.N.M. (2006) A Jfunction for marked point patterns. AISM, 58, 235259. DOI 10.1007/s1046300500157
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  #Sets C and D with independent NHPPs
set.seed(123)
lambda1<runif(500, 0.05, 0.1)
set.seed(124)
lambda2<runif(500, 0.01, 0.2)
pos1<simNHPc(lambda=lambda1, fixed.seed=123)$posNH
pos2<simNHPc(lambda=lambda2, fixed.seed=123)$posNH
aux<NHD(lambdaC=lambda1, lambdaD=lambda2, posC=pos1, typeC=1, posD=pos2, typeD=1)
aux$NHDr
#Example with independent NHPPs
#pos3<simNHPc(lambda=lambda1, fixed.seed=321)$posNH
#pos4<simNHPc(lambda=lambda2, fixed.seed=321)$posNH
#aux<NHD(lambdaC=cbind(lambda1,lambda2),lambdaD=cbind(lambda1,lambda2),posC=c(pos1,pos2),
# typeC=c(rep(1, length(pos1)), rep(2, length(pos2))), posD=c(pos3, pos4),
# typeD=c(rep(1, length(pos3)), rep(2, length(pos4))))
#aux$NHDr

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