# Hyper-class

From distr v2.6
by Peter Ruckdeschel

##### Class "Hyper"

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 $x = 0, ..., k$.
C.f. `rhyper`

- Keywords
- distribution

##### 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

##### See Also

`HyperParameter-class`

`DiscreteDistribution-class`

`Naturals-class`

`rhyper`

##### Examples

```
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.
```

*Documentation reproduced from package distr, version 2.6, License: LGPL-3*

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