dhyper(q, m, n, k, log = FALSE) phyper(q, m, n, k) qhyper(p, m, n, k) rhyper(nn, m, n, k, bigdata=F)
bdVector of values of a random variable representing the number of red balls
out of a sample of size
k drawn from an urn containing
m red balls and
n black ones.
bdVector of probabilities. Missing values (
NAs) are allowed. Its values should be between 0 and 1.
nn random hypergeometrically distributed numbers are returned
unless
length(nn) is larger than 1, in which case
length(nn) random numbers
are returned.
bdVector with non-negative integer elements.
bdVector with non-negative integer elements.
m red and
n black balls. This can be a vector or
bdVector like
m and
n.
TRUE, an object of type
bdVector is returned.
Otherwise, a
vector object is returned. This argument can be used only if the bigdata library section has been loaded.
TRUE, dhyper will return the log of the
density, not the density itself.
dhyper returns discrete probability values.
Other functions return vectors or
bdVectors of cumulative probabilities (
phyper), quantiles
(
qhyper), or random samples (
rhyper) for the Hypergeometric distribution.
rhyper causes creation of the dataset
.Random.seed if it does
not already exist, otherwise its value is updated.
Missing values (
NAs) and
+-Infs
are allowed as components of
q,
p or
nn,
but not in the vectors or
bdVectors of parameters.
If
q,
m,
n
, or
k are vectors or
bdVectors of different lengths, each is
replicated cyclically to the length of
the longest.
The values of
q,
m
,
n, and
k
are rounded to the nearest integer value before any calculations are made.
The Hypergeometric distribution can be described
by an Urn Model with
m red and
n black balls.
Any sequence of
k drawings resulting in
k-q black and
q red balls
has the same probability. It is similar to the Binomial distribution
but sampled from a finite population without replacement.
A hypergeometric variable corresponds to the conditional distribution
of the number in
the upper left cell of a 2 by 2 table with row marginal totals
m and
n
and column marginal totals
k and
N-k,
if the unconditional distributions of cell counts are
Poisson,
where
N=m+n is the grand total.
By symmetry between rows and columns,
phyper(q, m, n, k) = phyper(q, k, N-k, m).
The range of the distribution is
max(0, k-n) <= q <= min(m, k),
the density is
p(q, m, n, k) = choose(m, q) * choose(n, k-q) / choose(N, k),
the expected value is
m * k / N,
and variance is
m * n * k * (N-k) / (N^2 * (N-1)).
For details on the uniform random number generator implemented in S-PLUS,
see the
set.seed help file.
Hoel, P., Port, S. and Stone, C. (1971).
Introduction to Probability Theory. Houghton-Mifflin, Boston, MA.
Johnson, N. L. and Kotz, S. (1970).
Discrete Univariate Distributions, vol. 2.
Houghton-Mifflin, Boston, MA.
cumsum(dhyper(0:5,4,6,7)) # cumulative distribution function phyper(0:5,4,6,7) # same thing phyper(0:5,7,3,4) # same thing, by symmetry of rows and columns rhyper(10,4,6,7) # 10 random values dhyper(rep(3,3), m=c(5,8,12), n=4, k=4)