Hyper-class | R Documentation |
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
.
C.f. rhyper
Objects can be created by calls of the form Hyper(m, n, k)
.
This object is a hypergeometric distribution.
img
Object of class "Naturals"
: The space of the image of this
distribution has got dimension 1 and the name "Natural Space".
param
Object of class "HyperParameter"
: the parameter of this distribution (m
, n
, k
),
declared at its instantiation
r
Object of class "function"
: generates random numbers (calls function rhyper
)
d
Object of class "function"
: density function (calls function dhyper
)
p
Object of class "function"
: cumulative function (calls function phyper
)
q
Object of class "function"
: inverse of the cumulative function (calls function qhyper
).
The \alpha
-quantile is defined as the smallest value x
such that
p(x) \ge \alpha]
, where p
is the cumulative function.
support
:Object of class "numeric"
: a (sorted) vector containing the support of the discrete
density function
.withArith
logical: used internally to issue warnings as to interpretation of arithmetics
.withSim
logical: used internally to issue warnings as to accuracy
.logExact
logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExact
logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetry
object of class "DistributionSymmetry"
;
used internally to avoid unnecessary calculations.
Class "DiscreteDistribution"
, directly.
Class "UnivariateDistribution"
, by class "DiscreteDistribution"
.
Class "Distribution"
, by class "DiscreteDistribution"
.
signature(.Object = "Hyper")
: initialize method
signature(object = "Hyper")
: returns the slot m
of the parameter of the distribution
signature(object = "Hyper")
: modifies the slot m
of the parameter of the distribution
signature(object = "Hyper")
: returns the slot n
of the parameter of the distribution
signature(object = "Hyper")
: modifies the slot n
of the parameter of the distribution
signature(object = "Hyper")
: returns the slot k
of the parameter of the distribution
signature(object = "Hyper")
: modifies the slot k
of the parameter of the distribution
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
HyperParameter-class
DiscreteDistribution-class
Naturals-class
rhyper
H <- Hyper(m=3,n=3,k=3) # H is a hypergeometric distribution with m=3,n=3,k=3.
r(H)(1) # one random number generated from this distribution, e.g. 2
d(H)(1) # Density of this distribution is 0.45 for x=1.
p(H)(1) # Probability that x<1 is 0.5.
q(H)(.1) # x=1 is the smallest value x such that p(H)(x)>=0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
m(H) # m of this distribution is 3.
m(H) <- 2 # m of this distribution is now 2.
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