# Class "Hyper"

### Description

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*.
C.f. `rhyper`

### Objects from the Class

Objects can be created by calls of the form `Hyper(m, n, k)`

.
This object is a hypergeometric distribution.

### Slots

`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) >= 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.

### Extends

Class `"DiscreteDistribution"`

, directly.

Class `"UnivariateDistribution"`

, by class `"DiscreteDistribution"`

.

Class `"Distribution"`

, by class `"DiscreteDistribution"`

.

### Methods

- initialize
`signature(.Object = "Hyper")`

: initialize method- m
`signature(object = "Hyper")`

: returns the slot`m`

of the parameter of the distribution- m<-
`signature(object = "Hyper")`

: modifies the slot`m`

of the parameter of the distribution- n
`signature(object = "Hyper")`

: returns the slot`n`

of the parameter of the distribution- n<-
`signature(object = "Hyper")`

: modifies the slot`n`

of the parameter of the distribution- k
`signature(object = "Hyper")`

: returns the slot`k`

of the parameter of the distribution- k<-
`signature(object = "Hyper")`

: modifies the slot`k`

of the parameter of the distribution

### Author(s)

Thomas Stabla statho3@web.de,

Florian Camphausen fcampi@gmx.de,

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,

Matthias Kohl Matthias.Kohl@stamats.de

### See Also

`HyperParameter-class`

`DiscreteDistribution-class`

`Naturals-class`

`rhyper`

### Examples

1 2 3 4 5 6 7 | ```
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.
m(H) # m of this distribution is 3.
m(H) <- 2 # m of this distribution is now 2.
``` |