Runuran (version 0.40)

udnbinom: 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)

Value

An object of class "unuran.discr".

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. 0 < prob <= 1.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

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).

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

unuran.discr.

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)