1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
|
\name{Hyper-class}
\docType{class}
\alias{Hyper-class}
\alias{Hyper}
\alias{initialize,Hyper-method}
\title{Class "Hyper" }
\description{ The hypergeometric distribution is used for sampling \emph{without}
replacement. The density of this distribution with parameters
\code{m}, \code{n} and \code{k} (named \eqn{Np}, \eqn{N-Np}, and
\eqn{n}, respectively in the reference below) is given by
\deqn{
p(x) = \left. {m \choose x}{n \choose k-x} \right/ {m+n \choose k}%
}{p(x) = choose(m, x) choose(n, k-x) / choose(m+n, k)}
for \eqn{x = 0, \ldots, k}{x = 0, ..., k}.
C.f. \code{\link[stats:Hypergeometric]{rhyper}}
}
\section{Objects from the Class}{
Objects can be created by calls of the form \code{Hyper(m, n, k)}.
This object is a hypergeometric distribution.
}
\section{Slots}{
\describe{
\item{\code{img}}{Object of class \code{"Naturals"}: The space of the image of this
distribution has got dimension 1 and the name "Natural Space". }
\item{\code{param}}{Object of class \code{"HyperParameter"}: the parameter of this distribution (\code{m}, \code{n}, \code{k}),
declared at its instantiation }
\item{\code{r}}{Object of class \code{"function"}: generates random numbers (calls function \code{rhyper}) }
\item{\code{d}}{Object of class \code{"function"}: density function (calls function \code{dhyper}) }
\item{\code{p}}{Object of class \code{"function"}: cumulative function (calls function \code{phyper}) }
\item{\code{q}}{Object of class \code{"function"}: inverse of the cumulative function (calls function \code{qhyper}).
The \eqn{\alpha}{alpha}-quantile is defined as the smallest value \eqn{x} such that
\eqn{p(x) \ge \alpha]}{p(x) >= alpha}, where \eqn{p} is the cumulative function. }
\item{\code{support}:}{Object of class \code{"numeric"}: a (sorted) vector containing the support of the discrete
density function}
\item{\code{.withArith}}{logical: used internally to issue warnings as to
interpretation of arithmetics}
\item{\code{.withSim}}{logical: used internally to issue warnings as to
accuracy}
\item{\code{.logExact}}{logical: used internally to flag the case where
there are explicit formulae for the log version of density, cdf, and
quantile function}
\item{\code{.lowerExact}}{logical: used internally to flag the case where
there are explicit formulae for the lower tail version of cdf and quantile
function}
\item{\code{Symmetry}}{object of class \code{"DistributionSymmetry"};
used internally to avoid unnecessary calculations.}
}
}
\section{Extends}{
Class \code{"DiscreteDistribution"}, directly.\cr
Class \code{"UnivariateDistribution"}, by class \code{"DiscreteDistribution"}.\cr
Class \code{"Distribution"}, by class \code{"DiscreteDistribution"}.
}
\section{Methods}{
\describe{
\item{initialize}{\code{signature(.Object = "Hyper")}: initialize method }
\item{m}{\code{signature(object = "Hyper")}: returns the slot \code{m} of the parameter of the distribution }
\item{m<-}{\code{signature(object = "Hyper")}: modifies the slot \code{m} of the parameter of the distribution }
\item{n}{\code{signature(object = "Hyper")}: returns the slot \code{n} of the parameter of the distribution }
\item{n<-}{\code{signature(object = "Hyper")}: modifies the slot \code{n} of the parameter of the distribution }
\item{k}{\code{signature(object = "Hyper")}: returns the slot \code{k} of the parameter of the distribution }
\item{k<-}{\code{signature(object = "Hyper")}: modifies the slot \code{k} of the parameter of the distribution }
}
}
\author{
Thomas Stabla \email{statho3@web.de},\cr
Florian Camphausen \email{fcampi@gmx.de},\cr
Peter Ruckdeschel \email{peter.ruckdeschel@uni-oldenburg.de},\cr
Matthias Kohl \email{Matthias.Kohl@stamats.de}
}
\seealso{
\code{\link{HyperParameter-class}}
\code{\link{DiscreteDistribution-class}}
\code{\link{Naturals-class}}
\code{\link[stats:Hypergeometric]{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.
## 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.
}
\keyword{distribution}
\concept{discrete distribution}
\concept{lattice distribution}
\concept{Hypergeometric distribution}
\concept{S4 parameter class}
\concept{generating function}
|
