qp_pi: Simple uncalibrated prediction intervals for quasi-Poisson...

In predint: Prediction Intervals

Simple uncalibrated prediction intervals for quasi-Poisson data

Description

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).

Usage

qp_pi(
  newoffset,
  histoffset,
  lambda,
  phi,
  q = qnorm(1 - 0.05/2),
  alternative = "both",
  adjust = NULL,
  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
adjust	only important if called via quasi_pois_pi()
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

Details

This function returns a simple uncalibrated prediction interval

[l,u]_m = n^*_m \hat{\lambda} \pm q \sqrt{n^*_m \hat{\phi} \hat{\lambda} + \frac{n^{*2}_m \hat{\phi} \hat{\lambda}}{\sum_h n_h}}

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.

Value

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

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)

predint documentation built on Aug. 8, 2025, 6:40 p.m.