GenEnv.fun: Calculation of simulated envelopes

Description

This function calculates a point estimation and an envelope for a given statistic using a Monte Carlo approach. The statistic must be a function of the occurrence points of a NHPP.

It calls the auxiliary function funSim.fun (not intended for the users), see Details section.

Usage

GenEnv.fun(nsim, lambda, fun.name, fun.args = NULL, clevel = 0.95, 
cores = 1, fixed.seed=NULL)

Value

A list with elements

valmed: Point estimation (mean value) of the statistic to be calculated.
valinf: Lower value of the simulated CI.
valsup: Upper value of the simulated CI.
lambda: Input argument.
nsim: Input argument.
nsimval: Number of valid simulations (used in the calculation of the CI and the point estimation).
fixed.seed: Input argument.

Arguments

nsim: Number of simulations for the calculations.
lambda: Numeric vector of the intensity \(\lambda(t)\) (or \(\hat \lambda(t)\)) of the NHPP.
fun.name: Name of the function defining the statistic to be estimated.
fun.args: Additional arguments for the function fun.name.
clevel: Confidence level of the envelope.
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.

Details

The auxiliary function funSim.fun generates a simulated sample of the occurrence points in a NHPP and calculates the corresponding statistic using the simulated points.

Examples

Run this code

# Calculation of the point estimation and a 95% CI based on 100 simulations 
#for the second occurrence time of a NHPP with intensity lambdat.
#posk.fun(x, k) is a function that returns the value in the row k of vector x.

lambdat<-runif(1000,0.01,0.02)
aux<-GenEnv.fun(lambda=lambdat,fun.name="posk.fun",fun.args=2,nsim=100)

#if we want reproducible results, we can fixed the seed in the generation process
#(the number of cores used in the calculations must also be the same to reproduce 
#the result)

aux<-GenEnv.fun(lambda=lambdat,fun.name="posk.fun",fun.args=2,nsim=100,fixed.seed=123)

#the result (with 1 core): Lower interval:  25.55; Mean value:  136.06; Upper interval:  288