UNU.RAN random variate generator for the Negative Binomial
distribution with with parameters size and prob.
It also allows sampling from the truncated distribution.
[Special Generator] -- Sampling Function: Negative Binomial.
urnbinom(n, size, prob, lb = 0, ub = Inf)
size of required sample.
target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive.
probability of success in each trial. 0 < prob <= 1.
lower bound of (truncated) distribution.
upper bound of (truncated) distribution.
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
The Negative Binomial distribution with size \(= n\) and
prob \(= p\) has density
$$
p(x) = \frac{\Gamma(x+n)}{\Gamma(n) x!} p^n (1-p)^x
$$
for \(x = 0, 1, 2, \ldots\), \(n > 0\) and \(0 < p \le 1\).
This represents the number of failures which occur in a sequence of
Bernoulli trials before a target number of successes is reached.
The generation algorithm uses guide table based inversion when the
tails are not too heavy and method ‘DARI’ otherwise.
The parameters lb and ub can be used to generate
variates from the Negative Binomial distribution truncated to the
interval (lb,ub).
W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg
runif and .Random.seed about random number
generation, unuran for the UNU.RAN class, and
rnbinom for the R built-in generator.
## Create a sample of size 1000
x <- urnbinom(n=1000,size=10,prob=0.3)
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