qp_pi function

Simple uncalibrated prediction intervals for quasi-Poisson data

qp_pi() is a helper function that is internally called by quasi_pois_pi(). It calculates simple uncalibrated prediction intervals for Poisson data with constant overdispersion (quasi-Poisson assumption).

qp_pi(
  newoffset,
  histoffset,
  lambda,
  phi,
  q = qnorm(1 - 0.05/2),
  alternative = "both",
  newdat = NULL,
  histdat = NULL,
  algorithm = NULL
)

Arguments

• newoffset: number of experimental units in the future clusters
• histoffset: number of experimental units in the historical clusters
• lambda: overall Poisson mean
• phi: dispersion parameter
• q: quantile used for interval calculation
• alternative: either "both", "upper" or "lower" alternative specifies, if a prediction interval or an upper or a lower prediction limit should be computed
• newdat: additional argument to specify the current data set
• histdat: additional argument to specify the historical data set
• algorithm: used to define the algorithm for calibration if called via quasi_pois_pi(). This argument is not of interest for the calculation of simple uncalibrated intervals

Returns

qp_pi returns an object of class c("predint", "quasiPoissonPI").

Details

This function returns a simple uncalibrated prediction interval

with $n^*_m$ as the number of experimental units in the $m=1, 2, ... , M$ future clusters, $\hat{\lambda}$ as the estimate for the Poisson mean obtained from the historical data, $\hat{\phi}$ as the estimate for the dispersion parameter and $n_h$ as the number of experimental units per historical cluster.

The direct application of this uncalibrated prediction interval to real life data is not recommended. Please use the quasi_pois_pi_pi() functions for real life applications.

Examples

# Prediction interval
qp_pred <- qp_pi(newoffset=3, lambda=3, phi=3, histoffset=1:9, q=qnorm(1-0.05/2))
summary(qp_pred)