IndTestPP (version 3.0)

IntMPP: Simulated intervals in a vector of point processes

Description

This function calculates a point estimation and a confidence interval for a given parameter related to a vector of point processes using a Monte Carlo (or parametric bootstrap) approach. The estimator of the parameter must be a function of the occurrence points of the (possibly dependent) marginal processes of the vector of processes.

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

Usage

IntMPP(funMPP.name, funMPP.args, fun.name, fun.args = NULL, nsim=1000, clevel = 0.95, 
    cores = 1, fixed.seed = NULL)

Arguments

funMPP.name

Name of the function defining the distribution of the vector of point processes.

funMPP.args

Additional arguments for the function funMPP.name.

fun.name

Name of the function to calculate the estimation of the parameters. The first argument of this function must be a list called posNH.

fun.args

A list whose elements are the additional arguments for the function fun.name.

nsim

Number of simulations to be carried out.

clevel

Confidence level of the interval. A value in (0,1).

cores

Optional. Number of cores of the computer to be used in the calculations. Default: one core is used.

fixed.seed

An integer or NULL. If it is an integer, that is the value used to set the seed in random generation processes. It it is NULL, a random seed is used.

Value

A list with elements:

valmed

Point estimation (mean value) of the parameter.

valinf

Lower bound of the generated interval.

valsup

Upper bound of the generated interval.

nsim

Input argument.

fixed.seed

Input argument.

Details

This function calculates a point estimation and a confidence interval of a parameter related to a vector of point processes. It calls the auxiliary function funMPPGen, which generates a sample of vectors of processes using a parametric model. The parameter of interest is estimated using each process in that sample, so that a sample of values of the estimator is obtained. The mean of that sample is the point estimator, and the adequate sample percentiles give the lower and upper bounds of the confidence interval.

The parametric model is specified by the arguments funMPP.name and funMPP.args. Functions DepNHCPSP, DepNHNeyScot, DepNHPPqueue and DepNHPPMarked can be used as input of the argument funMPP.name to generate the corresponding vector of processes.

The considered estimator must be a function of the occurrence points of the vector of processes and any additional arguments, provided by argument fun.args, which must be a list. The first argument of the function fun.name must be a list called posNH whose elements are numeric vectors containing the occurrence points of each point process in the vector. For example, the first element of the output list of DepNHCPSP can be used as first argument of fun.name.

Examples

# NOT RUN {
# Calculation of the point estimation and  95% intervals based on 1000 simulations 
#of the   number of accurrences in each marginal process of a bivariate  Neyman-Scot process
# in  the time interval [100,200]
#NumI calculates the   number of occurrences in interval I in each element of  the list posNH

set.seed(123)
lambdai<-runif(1000,0.01,0.02)

aux<-IntMPP(funMPP.name="DepNHNeyScot", funMPP.args=list(lambdaParent=lambdai,d=2, 
  lambdaNumP=c(2,1), dplot=FALSE), fun.name="NumI", fun.args = list(I=c(100,200)), 
  fixed.seed = 125) 


# Calculation of the point estimation and a 95% interval based on 1000 simulations 
#of the  first occurrence time in  a multivariate  CPSP with d=3
#firstt calculates the  minimim occurrence time of  all the elements in the list posNH

#set.seed(124)
#lambdaij<-runif(1000,0.005,0.02)
#set.seed(125)
#lambdaijk<-runif(1000,0.001,0.02)
#lambdaiM<-cbind(lambdai,lambdai, lambdai, lambdaij, lambdaij, lambdaij, lambdaijk)
#aux<-IntMPP(funMPP.name="DepNHCPSP",funMPP.args=list(lambdaiM=lambdaiM,d=3,dplot=FALSE), 
#  fun.name="firstt", fixed.seed = 125) 


# }