uniongentri: Calculating the set of close points

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

Description

This function calculates the set of close points of each occurence point in the first process of a vector of two or three processes.

Usage

uniongentri(posx, posy, posz=NULL,  info = FALSE, PA = FALSE,
	procName=c('X','Y','Z'),...)

Arguments

posx	Numeric vector. Position of the occurrence points in the first process.
posy	Numeric vector. Position of the occurrence points in the second process.
posz	Optional. Numeric vector. Position of the occurrence points in the third process. Only used when three processes are involved.
info	Optional. Logical flag. If it is TRUE, information about the generated points is shown on the screen and dotcharts and bivariate charts of the occurrence points in the processes are displayed.
procName	Vector of character strings. Names of the processes.
PA	Optional. Logical flag. If it is TRUE, the close point relation is broadened by including the previous and the following points to the overlapping intervals.
...	Further arguments to be passed to the function plot if info=T.

Details

A point in a process is close to a point in another process, if their time intervals overlap; the time interval of a point is the interval between itself and the previous point in the same process. If there are three processes, the set of close points of t_{x_k},S_{x_i; xyz}, is defined as the set of the pairs of points (t_{y_j}, t_{z_k}) such that t_{x_i} is close to t_{y_j} and t_{y_j} is close to t_{z_k}. If there are two processes, S_{x_i; xy} is the set of points t_{y_j} such that t_{x_i} is close to t_{y_j}. This definition can be broadened, see argument PA, by adding to the set two more points, the previous and the following ones.

The algortihm to calculate the sets of close points (in the case of three processes) is the following, see Abaurrea et al. (2015) for details: First, given two processes, the pairs of close points in those processes are calculated. If the last point occurs in the first process, there is a censored time interval in the second process (the point overlaps a time interval whose occurrence point has not been observed) and that pair is not considered). This step is performed for all the combinations of pairs of processes. The basic close point relation is commutative, and only three different pairs (XY, YZ, XZ) must be considered. This is not the case of the broadened definition, where the six pairs (XY, YX, YZ, ZY, XZ, ZX) must be calculated.

Once all the pairs of close points are obtained, the set of close points for each point t_{x_i} is obtained by concatenating the adequate pairs of points from all the possible orders of the three processes: XYZ, XZY and YXZ for the basic definition, and the six possible permutations for the broadened definition. The final set of close points of t_{x_i} is the union of the different pairs from all the possible permutations.

Value

A list with elements:

X	First elements of the 3-tuples of points (t_{x_i}, t_{y_i}, t_{z_i}) in the sets of close points.
iX	Position i (=1,2,3....) of the point t_{x_i} in the first process.
Y	Second elements of the 3-tuples of points (t_{x_i}, t_{y_i}, t_{z_i}) in the sets of close points.
iY	Position i (=1,2,3....) of the point t_{y_i} in the second process.
Z	Third elements of the 3-tuples of points (t_{x_i}, t_{y_i}, t_{z_i}) in the sets of close points. It is NULL if posz=NULL.
iZ	Position i (=1,2,3....) of the point t_{z_i} in the third process. It is NULL if posz=NULL.

References

Abaurrea, J. Asin, J. and Cebrian, A.C. (2015). A Bootstrap Test of Independence Between Three Temporal Nonhomogeneous Poisson Processes and its Application to Heat Wave Modeling. Environmental and Ecological Statistics.

See Also

TestIndNH, DistSim, DistObs

Examples

set.seed(123)
posx<-sort(runif(20,0,1000))
posy<-sort(runif(25,0,1000))
posz<-sort(runif(40,0,1000))
aux<-uniongentri(posx, posy, posz, info=TRUE)

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