NHD {IndTestPP} | R Documentation |
Estimating the D-function
Description
This function estimates
the cross nearest neighbour distance distribution function, D, between
two sets, C
and D
, of (homogenous or nonhomogeneous) point processes.
The D-function 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.
Usage
NHD(lambdaC, lambdaD, T=NULL,Ptype='inhom', posC, typeC=1, posD, typeD=1,
r = NULL, dplot = TRUE, tit = "D(r)",...)
Arguments
lambdaC |
A matrix of positive values. Each column is the intensity vector of one of the point processes in
|
lambdaD |
A matrix of positive values. Each column is the intensity vector of one of the point process in
|
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 |
posC |
Numeric vector. Occurrence times of the points in all the point processes in |
typeC |
Numeric vector with the same length as |
posD |
Numeric vector. Occurrence times of the points in all the point processes in |
typeD |
Numeric vector with the same length as |
r |
Numeric vector. Values where the D-function must be evaluated. If it is NULL, a default vector is used, see Details. |
dplot |
Optional. A logical flag. If it is TRUE, the D-function is plotted. |
tit |
Optional. The title to be used in the plot of the D-function. |
... |
Further arguments to be passed to the function |
Details
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 D-function between
two sets, C
and D
, of (homogenous or nonhomogeneous) point processes, see
Cebrian et al (2020) for details of the estimation. The D-function 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 D-function suggest few points in processes in D
in the r-neighbourhood
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 J-functions 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)
Value
A list with elements:
r |
Vector of values |
NHDr |
Estimated values of |
T |
Length of the observed period. |
References
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 J-function for marked point patterns. AISM, 58, 235-259. DOI 10.1007/s10463-005-0015-7
See Also
Examples
#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