DistSim: Generates a vector of independent processes, and calculates...

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

Description

This function generates a vector of two (or three) independent homogeneous or nonhomogeneous processes conditionally on the first one, by simulating the second (and the third) process using a parametric model (Poisson processes or Neyman-Scott cluster processes).

It also calculates the set of close points and the mean distance in the generated vector, for each point t_{x_i} in the first process.

DistSimfix allows to fix a seed in the generation process.

Usage

DistSim(posx, NumProcess=2, type = "Poisson", lambdaMarg = NULL, 
	lambdaParent = NULL, lambdaNumP=NULL, dist = "normal", sigmaC = 1, 
	minC = -1, maxC = 1, PA = FALSE,info=FALSE,...)

DistSimfix(posx, NumProcess=2, type = "Poisson", lambdaMarg = NULL, 
	lambdaParent = NULL,lambdaNumP=NULL, dist = "normal", sigmaC = 1, 
	minC = -1, maxC = 1, PA = FALSE,info=FALSE,fixed.seed=1,...)

Arguments

posx	Numeric vector. Position of the occurrence points in the first process.
NumProcess	Optional. Integer equal to 2 or 3, the number of processes in the vector.
type	Optional. Label "Poisson" or "PoissonCluster". Type of point processes to be generated. Up to now, only two types are available: Poisson processes ("Poisson") and Neyman-Scott cluster processes ("PoissonCluster").
lambdaMarg	Two-column matrix. Only used when type="Poisson". Each column is the intensity λ (t) used to generate the processes.
lambdaParent	Numeric vector. Only used when type="PoissonCluster". Intensity values of the Poisson process used to generate the centres of the clusters of the Neyman-Scott process.
lambdaNumP	Numeric vector (length ≤ 2). Only used when type="PoissonCluster". Mean values of the number of sons in each process. If its length is 1 and NumProcess=2, the same value is used for both processes.
dist	Optional. Label "normal" or "uniform". Only used when type="PoissonCluster". Distribution used to generate the point distances in each cluster.
sigmaC	Optional. Numeric vector. Only used when type="PoissonCluster" and dist="normal". Standard deviation of the normal distribution. If its length is 1 and NumProcess=2, the same value is used for both processes.
minC	Optional. Numeric vector. Only used when type="PoissonCluster" and dist="uniform". Lower bounds of the Uniform distribution. If its length is 1 and NumProcess=2, the same value is used for both processes.
maxC	Optional. Numeric vector. Only used when type="PoissonCluster" and dist="uniform". Upper bounds of the Uniform distribution. If its length is 1 and NumProcess=2, the same value is used for both 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.
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 of the three processes are displayed.
fixed.seed	Optional. Only available in DistSimfix. Integer value used to set the seed in random generation procedures.
...	Further arguments to be passes to the functions plot and dotchart if argument info=T.

Details

This function is mainly used in the application of a parametric bootstrap approach to generate a pair of independent processes with the same marginal distributions than the observed ones. To that aim, the first process is fixed and the others are generated using a parametric model. These processes are used for example to build a test to assess the independecne between two or three processes, see TestIndNH.

Two types of processes (Poisson, "Poisson", and Neyman-Scott cluster processes,"PoissonCluster") can be generated. Generation of nonhomogeneous Poisson processes is done using the inversion algorithm, see simNHPc. For generation of Neyman-Scott processes, see IndNHNeyScot.

The function also calculates the set of close points and the mean distance for each point t_{x_i} in the first process, in the new generated vector of processes.

The lenght of the period where the processes are generated is determined by the length of the argument lambdaParent or the number of rows of lambdaMarg. Homogenous processes are generated if the intensity vectors in lambdaParent or in lambdaMarg are constant (that is if all the values in the vector are equal).

If a seed must be fixed in the generation process, function DistSimfix has to be used. The functions DistSim and DistSimfix are similar, the difference is that the first one uses a random seed to generate the processes, while the second one uses a seed set by the argument fixed.seed.

Value

DistTri

Vector of the mean distances of each point t_{x_i} calculated in the generated processes.

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, 22(1), 127-144.

See Also

TestIndNH, DistObs, IndNHNeyScot, simNHPc

Examples

#Calculation of the distances in a vector of  three independent Poisson processes   
#conditionally to the first one

set.seed(123)
lambdax<-runif(200, 0.01,0.15)
posaux<-simNHPc(lambda=lambdax, fixed.seed=123)$posNH

set.seed(124)
lambday<-runif(200, 0.005,0.1)
set.seed(125)
lambdaz<-runif(200, 0.005,0.2)

DistSimfix(posx=posaux, type = "Poisson", lambdaMarg = cbind(lambday,lambdaz), 
	fixed.seed=123, info=TRUE)
#DistSim(posx=posaux, type = "Poisson", lambdaMarg = cbind(lambday,lambdaz))

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