# CPSPpoints: Identifying the occurrence points of the indicator processes... In IndTestPP: Tests of Independence and Analysis of Dependence Between Point Processes in Time

## Description

It calculates the occurrence points in the three indicator processes of a bivariate Common Poisson Shock Process (CPSP), using as input the two marginal processes N_1 and N_2.

## Usage

 `1` ```CPSPpoints(N1,N2,date=NULL, dplot=T, pmfrow=c(2,1), axispoints=NULL,...) ```

## Arguments

 `N1` Binary vector of the first CPSP marginal process; occurrence points must be marked with 1 and the other with 0. `N2` Binary vector of the second CPSP marginal process; occurrence points must be marked with 1 and the other with 0. `date` Optional. A vector or matrix indicating the date of each observation. `dplot` Optional. A logical flag. If it is TRUE, the marginal and indicator processes are plotted. `pmfrow` Optional. A vector of the form (nr, nc) to be supplied as value of the argument `mfrow` in `par`. `axispoints` Optional. Numeric vector with the points in the time index where axis ticks and labels (from the first column in `date`) have to be drawn. `...` Further arguments to be passed to the function `plot`.

## Details

A bivariate CPSP N is usually specified by its two marginal, and possibly dependent, processes N_1 and N_2, which are the observed processes. However, N can be decomposed into three independent indicator processes: N_{(1)}, N_{(2)} and N_{(12)}, which are the processes of the points occurring only in the first marginal process, only in the second and in both of them (simultaneous points). The union of N_{(1)} and N_{(12)}, and N_{(2)} and N_{(12)} gives respectively the two marginal processes.

The points in the marginal N_{1}, N_{2} and indicator N_{(1)}, N_{(2)} and N_{(12)} processes can be optionally plotted. If `date` is NULL, default axis are used. Otherwise, the values in `axispoints` are used as the points in the time index where axis ticks and labels, from the first column in `date`, have to be drawn. If `axispoints` is NULL, a default grid of points is built using the function `marca`.

## Value

A list with components

 `Px1` Vector of the occurrence points in N_{(1)}. `Px2` Vector of the occurrence points in N_{(2)}. `Px12` Vector of the occurrence points in N_{(12)}. `N1` Input argument. `N2` Input argument. `date` Input argument.

## 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.

`CPSPPOTevents`, `PlotMCPSP`, `PlotICPSP`
 ```1 2 3 4 5 6``` ```set.seed(123) X<-as.numeric(runif(100)<0.10) set.seed(124) Y<-as.numeric(runif(100)<0.15) aux<-CPSPpoints(N1=X,N2=Y) ```