IndTestPP (version 3.0)

DepNHCPSP: Generating a Common Poisson Shock Process

Description

This function generates the \(d\) marginal processes of a Common Poisson Shock Process, which are \(d\) dependent Poisson processes. Both homogeneous and nonhomogeneous processes can be generated. In the case \(d=2\), the processes can be optionally plotted.

Usage

DepNHCPSP(lambdaiM, d,dplot=TRUE, pmfrow=c(2,1), fixed.seed = NULL, ...)

Arguments

lambdaiM

Matrix. Each column contains the intensity values of a indicator process .

d

Numeric value. Dimension (number of marginal processes) of the CPSP.

dplot

Optional. A logical flag. If it is TRUE and d=2, the marginal and indicator processes are plotted.

pmfrow

Optional. A vector of the form (nr, nc) to be supplied as argument mfrow in par.

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.

Value

A list with elements

posNH

A list of d vectors containing the occurrence points of the d marginal processes. The name of the elements of the list are N1, N2...,Nd.

posNHG

A list of m vectors containing the occurrence points of the m indicator processes.

lambdaM

Matrix. Each column is the intensity vector of a marginal process.

Details

A CPSP \(N\) is usually specified by its marginal, and possibly dependent, processes \(N_1\), \(N_2\)..., \(N_d\), which are the observed processes. However, \(N\) can be decomposed into m independent indicator processes: \(N_{(1)}\), \(N_{(2)}\), ..., \(N_{(12)}\), ..., \(N_{(1...d)}\), which are the processes of the points occurring only in the first marginal process, only in the second,..., simultaneously in the two first marginal processes, ... and in all the marginal processes simultaneously. The number of indicator processes is m, the sum of n choose i for \(i=1, ..., d\). The value m must also be the number of columns of the matrix in argument lambdaiM. The marginal process \(N_{i}\) is obtained as the union of all the indicator processes where the index i appears, \(N_{.i.}\). The intensity of \(N_{i}\) is the sum of the intensities of all the indicator processes \(N_{.i.}\).

The decomposition into indicator processes can be readily applied for the generation of a CPSP: it reduces to the generation of m independet PPs, see Cebrian et al. (2020) for details. Points are generated in continuous time.

In order to generate d independent Poisson processes, the function IndNHPP has be used.

In the bivariate case \(d=2\), the points in the marginal \(N_{1}\), \(N_{2}\) and indicator \(N_{(1)}\), \(N_{(2)}\) and \(N_{(12)}\) processes can be optionally plotted.

References

Abaurrea, J. Asin, J. and Cebrian, A.C. (2015). Modeling and projecting the occurrence of bivariate extreme heat events using a nonhomogeneous common Poisson shock process. Stochastic and Environmental Research and risk assessment, 29(1), 309-322.

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

See Also

DepNHNeyScot, DepNHPPqueue, DepNHPPMarked, IndNHPP

Examples

# NOT RUN {
set.seed(123)
lambdai1<-runif(200,0,0.1)
set.seed(124)
lambdai2<-runif(200,0,0.07)
set.seed(125)
lambdai12<-runif(200,0,0.05)
set.seed(126)
lambdai123<-runif(200,0,0.01)
lambdaiM<-cbind(lambdai1, lambdai2,lambdai1, lambdai12, lambdai12, lambdai12, lambdai123)
aux<-DepNHCPSP(lambdaiM=lambdaiM, d=3, fixed.seed=123)

#lambdaiM<-cbind(lambdai1, lambdai2, lambdai12)
#aux<-DepNHCPSP(lambdaiM=lambdaiM, d=2,fixed.seed=123, dplot=TRUE)
# }