IndNHNeyScot {IndTestPP}

Generating a vector of independent Neyman-Scott cluster processes

Description

This function generates a vector of d independent (homogeneous or nonhomogeneous) Neyman-Scott cluster processes with independent trajectories of cluster centers with the same intensity.

It calls the auxiliary function GenSons (not intended for the users), see Details.

Usage

IndNHNeyScot(lambdaParent, d, lambdaNumP = 1,  dist = "normal", 
	sigmaC = 1, minC = -1, maxC = 1, dplot=TRUE,fixed.seed=NULL,...)

Arguments

lambdaParent

Numeric vector. Intensity of the Poisson process used to generate the independent trajectories of the cluster centres of the Neyman-Scott process.

d

Integer. Number of independent processes to be generated.

lambdaNumP

Optional. Numeric vector. Mean values of the number of sons of each marginal process. If its length is equal to 1, the same value is used to generate all the processes.

dist

Optional. Label "normal" or "uniform". Distribution used to generate the point locations of each cluster.

sigmaC

Optional. Numeric vector. Standard deviation of the normal distribution. Only used if dist="normal". If its length is equal to 1, the same value is used in the d processes.

minC

Optional. Numeric vector. Lower bounds of the Uniform distribution. Only used if dist="uniform". If its length is equal to 1, the same value is used in the d processes.

maxC

Optional. Numeric vector. Upper bounds of the Uniform distribution. Only used if dist="uniform". If its length is equal to 1, the same value is used in the d processes.

dplot

Optional. A logical flag. If it is TRUE, the generated marginal processes are plotted.

fixed.seed

Optional. An integer or NULL. 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

A Neyman-Scott process is a Poisson cluster process where the points in each cluster are randomly distributed around the cluster center, see Neyman and Scott (1958) and Entekhabi et al. (1989).

To generate each process in the vector, an independent trajectory of the Poisson process of the cluster centres is generated first. Then, the number of points in each cluster is generated using a Poisson distribution with mean value \mu_{P_i} (i=1,...d). Finally, the distances to the centre of each point in the cluster is be generated using one of the two distributions available, N(0, sigmaC) or Uniform(minC, maxC).

The lenght of the period where the processes are generated is determined by the length of the argument lambdaParent.

Homogenous processes are generated if the intensity vector lambdaParent is constant (that is if all the values are equal).

The marginal processes of the generated vector can be optionally plotted.

Value

A list with elements:

posNH

A list of d vectors, each one containing the time occurrences of one of the marginal processes. The name of the elements of the list are N1, N2,...,Nd.

References

Cebrian, A.C., Abaurrea, J. and Asin, J. (2020). Testing independence between two point processes in time. Journal of Simulation and Computational Statistics.

Neyman, J., & Scott, E. L. (1958). Statistical approach to problems of cosmology. Journal of the Royal Statistical Society. Series B (Methodological), 1-43.

Entekhabi, D., Rodriguez-Iturbe, I., & Eagleson, P. S. (1989). Probabilistic representation of the temporal rainfall process by a modified Neyman-Scott Rectangular Pulses Model: Parameter estimation and validation. Water Resources Research, 25(2), 295-302.

See Also

DepNHNeyScot, IndNHPP

Examples

set.seed(123)
lambda<-runif(1000)/10

IndNHNeyScot(lambdaParent=lambda, d=3, lambdaNumP = c(2,3,2),  dist = "normal", 
	sigmaC = 2, fixed.seed=123)