Runuran (version 0.30)

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 $$ p(x) = \left. {m \choose x}{n \choose k-x} \right/ {m+n \choose k} $$ 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

# NOT RUN {
## 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)

# }