# 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)