Hypergeometric {base}

R Documentation

The Hypergeometric Distribution

Usage

dhyper(x, N1, N2, n)
phyper(q, N1, N2, n)
qhyper(p, N1, N2, n)
rhyper(nobs, N1, N2, n)

Arguments

x, q	vector of quantiles.
N1	the number of white balls in the population.
N2	the number of black balls in the population.
n	the number of balls drawn from the urn.
p	probability, it must be between 0 and 1.
nobs	the number of observations to be generated.

Value

These functions provide information about the hypergeometric distribution with parameters N1, N2 and n.

dhyper gives the density, phyper gives the distribution function qhyper gives the quantile function and rhyper generates random deviates.

The hypergeometric distribution is used for sampling without replacement. It has density

p(x) = \left. {N1 \choose x}{N2 \choose n-x} \right/ {N1+N2 \choose n}

for x = 0, \ldots, n.

Examples

N1 <- 10; N2 <- 7; n <- 8
x <- 0:N1
rbind(phyper(x, N1, N2, n), dhyper(x, N1, N2, n))
all(phyper(x, N1, N2, n) == cumsum(dhyper(x, N1, N2, n)))
# FALSE
# Relative Error :
formatC(signif((phyper(x, N1, N2, n) / cumsum(dhyper(x, N1, N2, n)) - 1), 2),
        format='g', dig=2)

---