DepCPSPNHK: Estimating cross K-function and envelopes for marginal...

In IndTestPP: Tests of Independence and Analysis of Dependence Between Point Processes in Time

Description

This function estimates the cross K-function between two (homogenous or nonhomogeneous) point processes in time, N_{x} and N_{y}. It is evaluated in a grid of distances r and plotted. An envelope built by simulation under the hypothesis that the processes are the marginal processes of a bivariate CPSP is also plotted.

It calls the auxiliary function DepCPSPKenv, not intended for users.

Usage

DepCPSPNHK(posx, posy, lambdaix, lambdaiy, lambdaixy, r=NULL, typeEst=1, 
                  nsim=1000, conf=0.95,tit=NULL, cores=1,fixed.seed=NULL,...)

Arguments

posx	Numeric vector. Occurrence times of the points in the first point process N_{x} .
posy	Numeric vector. Occurrence times of the points in the second point process N_{y} .
lambdaix	Numeric vector. Intensity values of N_{(x)}.
lambdaiy	Numeric vector. Intensity values of N_{(y)}.
lambdaixy	Numeric vector. Intensity values of N_{(xy)}.
r	Optional. Numeric vector. Grid values where the K-function must be evaluated. If it is NULL, a default vector is used; see Details.
typeEst	Optional. Two possible values: 1 or 2. They determines which one of the two available estimators of the function K_{ij} has to be used; see Details.
nsim	Optional. Numeric value. Number of simulations to obtain the envelope.
conf	Optional. Numeric value in (0,1). Confidence level of the envelope for the K-function.
tit	Optional. Title to be used in the plot of the K-function.
cores	Optional. Number of cores of the computer to be used in the calculations.
fixed.seed	An integer or NULL. If it is an integer, that is the value used to set the seed in random generation processes. If it is NULL, a random seed is used.
...	Further arguments to be passed to the function plot.

Details

This function estimates the cross K function between two (homogenous or nonhomogeneous) point processes in time, N_{x} and N_{y}. Two different estimators are available, see NHK for more details.

An envelope for the cross K function is built under the hypothesis that the processes are the marginal processes of a bivariate CPSP with intensities of the indicator processes lambdaxi, lambdayi and lambdaxyi. The envelope is based on the simulation of CPSPs, gnerated by function DepNHCPSP.

If argument r is NULL, the following r-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)

where T is the length of the observed period.

Value

A list with elements:

r	Vector of values r where the cross K-function is estimated.
NHKr	Estimated values of K_{ij}(r).
KenvL	Lower bounds of the envelope of K_{ij}(r).
KenvU	Upper bounds of the envelope of K_{ij}(r).
T	Length of the observed period of the processes.

See Also

NHK, DepNHCPSP

Examples

set.seed(123)
lambdai1<-runif(500,0.005,0.01)
set.seed(124)
lambdai2<-runif(500,0.005,0.01)
set.seed(125)
lambdai12<-runif(500,0.005,0.02)

#Observed process: independent Poisson processes
posx<-simNHPc(lambda = (lambdai1+lambdai12), fixed.seed = 13)$posNH
posy<-simNHPc(lambda = (lambdai2+lambdai12), fixed.seed = 14)$posNH
aux<-DepCPSPNHK(posx=posx, posy=posy, lambdaix=lambdai1, lambdaiy=lambdai2, 
	       lambdaixy=lambdai12, fixed.seed=123, r=c(1:10), nsim=500)

#Observed processes: dependent marginal processes of a CPSP
#pos<-DepNHCPSP(lambdaiM=cbind(lambdai1, lambdai2, lambdai12), d=2,
#	fixed.seed=123, dplot=F)$posNH
#aux<-DepCPSPNHK(posx=pos$N1, posy=pos$N2, lambdaix=lambdai1, 
#	lambdaiy=lambdai2, lambdaixy=lambdai12, fixed.seed=125, r=c(1:10))

IndTestPP documentation built on Aug. 29, 2020, 1:06 a.m.