NHPoisson (version 3.4)

transfH.fun: Transform a NHPP into a HPP

Description

This function transforms the points \(t^{NH}_i\) of a NHPP into the occurrence points \(t^{H}_i\) of a HPP of rate 1.

Usage

transfH.fun(mlePP)

Value

A list with elements

posEH

Numeric vector of the transformed occurrence times of the HPP.

posE

Slot of the input argument mlePP.

lambdafit

Slot of the input argument mlePP.

inddat

Slot of the input argument mlePP.

Arguments

mlePP

An object of class mlePP-class; usually, the output from fitPP.fun.

Details

Transformation of the NHPP points \(t^{NH}_i\) into the HPP points \(t^{H}_i\) is based on the time scale transformation, $$t^H_i=\int_0^{t^{NH}_i}\lambda(t)dt.$$ (usually the estimated value \(\hat \lambda(t)\) is used in the transformation.)

References

Cebrian, A.C., Abaurrea, J. and Asin, J. (2015). NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes. Journal of Statistical Software, 64(6), 1-24.

Cox, D.R., Isham, V., 1980. Point Processes. Chapman and Hall.

Daley, D. and D. Vere-Jones (2003). An Introduction to the Theory of Point Processes. Springer.

See Also

simNHP.fun

Examples

X1<-rnorm(500)
X2<-rnorm(500)
auxmlePP<-fitPP.fun(posE=round(runif(50,1,500)), inddat=rep(1,500),
	covariates=cbind(X1,X2),start=list(b0=1,b1=0,b2=0))


posEH<-transfH.fun(auxmlePP)