| Hypergeometric {stats} | R Documentation |
Density, distribution function, quantile function and random generation for the hypergeometric distribution.
dhyper(x, m, n, k, log = FALSE) phyper(q, m, n, k, lower.tail = TRUE, log.p = FALSE) qhyper(p, m, n, k, lower.tail = TRUE, log.p = FALSE) rhyper(nn, m, n, k)
x, q |
vector of quantiles representing the number of white balls drawn without replacement from an urn which contains both black and white balls. |
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. |
p |
probability, it must be between 0 and 1. |
nn |
number of observations. If |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
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) = choose(m, x) choose(n, k-x) / choose(m+n, k)
for x = 0, …, k.
The quantile is defined as the smallest value x such that F(x) ≥ p, where F is the distribution function.
dhyper gives the density,
phyper gives the distribution function,
qhyper gives the quantile function, and
rhyper generates random deviates.
Invalid arguments will result in return value NaN, with a warning.
dhyper computes via binomial probabilities, using code
contributed by Catherine Loader (see dbinom).
phyper is based on calculating dhyper and
phyper(...)/dhyper(...) (as a summation), based on ideas of Ian
Smith and Morten Welinder.
qhyper is based on inversion.
rhyper is based on a corrected version of
Kachitvichyanukul, V. and Schmeiser, B. (1985). Computer generation of hypergeometric random variates. Journal of Statistical Computation and Simulation, 22, 127–145.
Johnson, N. L., Kotz, S., and Kemp, A. W. (1992) Univariate Discrete Distributions, Second Edition. New York: Wiley.
Distributions for other standard distributions.
m <- 10; n <- 7; k <- 8 x <- 0:(k+1) rbind(phyper(x, m, n, k), dhyper(x, m, n, k)) all(phyper(x, m, n, k) == cumsum(dhyper(x, m, n, k)))# FALSE ## but error is very small: signif(phyper(x, m, n, k) - cumsum(dhyper(x, m, n, k)), digits=3)