qp_pi {predint} | R Documentation |
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",
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"
|
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
|
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)