CItran.fun: Confidence intervals for lambda(t) based on transformation In NHPoisson: Modelling and Validation of Non Homogeneous Poisson Processes

Description

Given the \hat β covariance matrix (or its estimation), an approximate confidence interval for each λ(t)=\exp(ν(t)) is calculated using a transformation of the confidence interval for the linear predictor ν(t)=\textbf{X(t)} β. The transformation is \exp(I_i), where I_i are the confidence limits of ν(t).

Usage

 1 CItran.fun(VARbeta, lambdafit, covariates, clevel = 0.95) 

Arguments

 VARbeta (Estimated) Coariance matrix of the \hat β parameter vector. lambdafit Numeric vector of fitted values of the PP intensity \hat λ(t). covariates Matrix of covariates to estimate the PP intensity. clevel Confidence level of the confidence intervals. A value in the interval (0,1).

Value

A list with elements

 LIlambda Numeric vector of the lower values of the intervals. UIlambda Numeric vector of the upper values of the intervals. lambdafit Input argument.

Note

fitPP.fun calls CItran.fun when the argument is CIty='Transf'.

References

Casella, G. and Berger, R.L., (2002). Statistical inference. Brooks/Cole.

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.

CIdelta.fun, fitPP.fun, VARbeta.fun
 1 2 aux<-CItran.fun(VARbeta=0.01, lambdafit=exp(rnorm(100)), covariates=matrix(rep(1,100)), clevel=0.95)