rnbinom | R Documentation |
rnbinom()
samples negative-binomial data.
The following description of the sampling process is based on the parametrization
used by Gsteiger et al. 2013.
rnbinom(n, lambda, kappa, offset = NULL)
n |
defines the number of clusters ( |
lambda |
defines the overall Poisson mean ( |
kappa |
dispersion parameter ( |
offset |
defines the number of experimental units per cluster ( |
The variance of the negative-binomial distribution is
var(Y_i) = n_i \lambda (1+ \kappa n_i \lambda).
Negative-biomial observations can be sampled based on predefined values of \kappa
,
\lambda
and n_i
:
Define the parameters of the gamma distribution as a=\frac{1}{\kappa}
and
b_i=\frac{1}{\kappa n_i \lambda}
. Then, sample the Poisson means for each cluster
\lambda_i \sim Gamma(a, b_i).
Finally, the observations y_i
are sampled from the Poisson distribution
y_i \sim Pois(\lambda_i)
rnbinom()
returns a data.frame
with two columns:
y
as the observations and offset
as the number of offsets per
observation.
Gsteiger, S., Neuenschwander, B., Mercier, F. and Schmidli, H. (2013): Using historical control information for the design and analysis of clinical trials with overdispersed count data. Statistics in Medicine, 32: 3609-3622. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.5851")}
# Sampling of negative-binomial observations
# with different offsets
set.seed(123)
rnbinom(n=5, lambda=5, kappa=0.13, offset=c(3,3,2,3,2))
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