Runuran (version 0.21.0)

udhyper: UNU.RAN object for Hypergeometric distribution

Description

Create UNU.RAN object for a Hypergeometric distribution with parameters m, n, and k. [Distribution] -- Hypergeometric.

Usage

udhyper(m, n, k, lb=max(0,k-n), ub=min(k,m))

Arguments

m

the number of white balls in the urn.

n

the number of black balls in the urn.

k

the number of balls drawn from the urn.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Value

• An object of class "unuran.discr".

Details

The Hypergeometric distribution is used for sampling without replacement. The density of this distribution with parameters m, n and k (named $Np$, $N-Np$, and $n$, respectively in the reference below) is given by $$p(x)=(\genfrac{}{}{0ex}{}{m}{x})(\genfrac{}{}{0ex}{}{n}{k-x})/(\genfrac{}{}{0ex}{}{m+n}{k})$$ for $x = 0, \ldots, k$.

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. Chap. 6, p. 237.

Examples

## Create distribution object for Hypergeometric distribution
dist <- udhyper(m=15,n=5,k=7)
## Generate generator object; use method DGT (inversion)
gen <- dgtd.new(dist)
## Draw a sample of size 100
x <- ur(gen,100)