nb_pi() is a helper function that is internally called by neg_bin_pi(). It
calculates simple uncalibrated prediction intervals for negative-binomial data
with offsets.
nb_pi(
newoffset,
histoffset,
lambda,
kappa,
q = qnorm(1 - 0.05/2),
alternative = "both",
newdat = NULL,
histdat = NULL,
algorithm = NULL
)np_pi returns an object of class c("predint", "negativeBinomialPI").
number of experimental units in the future clusters
number of experimental units in the historical clusters
overall Poisson mean
dispersion parameter
quantile used for interval calculation
either "both", "upper" or "lower".
alternative specifies, if a prediction interval or
an upper or a lower prediction limit should be computed
additional argument to specify the current data set
additional argument to specify the historical data set
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
This function returns a simple uncalibrated prediction interval $$[l,u]_m = n^*_m \hat{\lambda} \pm q \sqrt{n^*_m \frac{\hat{\lambda} + \hat{\kappa} \bar{n} \hat{\lambda}}{\bar{n} H} + (n^*_m \hat{\lambda} + \hat{\kappa} n^{*2}_m \hat{\lambda}^2) }$$
with \(n^*_m\) as the number of experimental units in \(m=1, 2, ... , M\) future clusters,
\(\hat{\lambda}\) as the estimate for the Poisson mean obtained from the
historical data, \(\hat{\kappa}\) as the estimate for the dispersion parameter,
\(n_h\) as the number of experimental units per historical cluster and
\(\bar{n}=\sum_h^{n_h} n_h / H\).
The direct application of this uncalibrated prediction interval to real life data
is not recommended. Please use the neg_bin_pi() function for real life applications.
# Prediction interval
nb_pred <- nb_pi(newoffset=3, lambda=3, kappa=0.04, histoffset=1:9, q=qnorm(1-0.05/2))
summary(nb_pred)
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