Hyper-class
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 \(x = 0, \ldots, k\).
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 instantiationr
Object of class
"function"
: generates random numbers (calls functionrhyper
)d
Object of class
"function"
: density function (calls functiondhyper
)p
Object of class
"function"
: cumulative function (calls functionphyper
)q
Object of class
"function"
: inverse of the cumulative function (calls functionqhyper
). 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.
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 slotm
of the parameter of the distribution- m<-
signature(object = "Hyper")
: modifies the slotm
of the parameter of the distribution- n
signature(object = "Hyper")
: returns the slotn
of the parameter of the distribution- n<-
signature(object = "Hyper")
: modifies the slotn
of the parameter of the distribution- k
signature(object = "Hyper")
: returns the slotk
of the parameter of the distribution- k<-
signature(object = "Hyper")
: modifies the slotk
of the parameter of the distribution
See Also
HyperParameter-class
DiscreteDistribution-class
Naturals-class
rhyper
Examples
# NOT RUN {
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.
# }