Runuran (version 0.21.0)

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)

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<="" code="">.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Value

• An object of class "unuran.discr".

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)