udnbinom {Runuran} | R Documentation |
UNU.RAN object for Negative Binomial distribution
Description
Create UNU.RAN object for a Negative Binomial distribution
with parameters size
and prob
.
[Distribution] – Negative Binomial.
Usage
udnbinom(size, prob, lb = 0, ub = Inf)
Arguments
size |
target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive. |
prob |
probability of success in each trial. |
lb |
lower bound of (truncated) distribution. |
ub |
upper bound of (truncated) distribution. |
Details
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 domain of the distribution can be truncated to the
interval (lb
,ub
).
Value
An object of class "unuran.discr"
.
Author(s)
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
References
N.L. Johnson, S. Kotz, and A.W. Kemp (1992): Univariate Discrete Distributions. 2nd edition, John Wiley & Sons, Inc., New York. Sect. 5.1, p. 200.
See Also
Examples
## Create distribution object for Negative Binomial distribution
dist <- udnbinom(size=100, prob=0.33)
## Generate generator object; use method DARI
gen <- darid.new(dist)
## Draw a sample of size 100
x <- ur(gen,100)