Nbinom-class {distr}R Documentation

Class "Nbinom"

Description

The negative binomial distribution with size = n, by default =1, and prob = p, by default =0.5, has density

d(x) = Gamma(x+n)/(Gamma(n) x!) p^n (1-p)^x

for x = 0, 1, 2, ...

This represents the number of failures which occur in a sequence of Bernoulli trials before a target number of successes is reached. C.f. rnbinom

Objects from the Class

Objects can be created by calls of the form Nbinom(prob, size). This object is a negative binomial 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 "NbinomParameter": the parameter of this distribution (prob, size), declared at its instantiation
r:
Object of class "function": generates random numbers (calls function rnbinom)
d:
Object of class "function": density function (calls function dnbinom)
p:
Object of class "function": cumulative function (calls function pnbinom)
q:
Object of class "function": inverse of the cumulative function (calls function qnbinom). The quantile is defined as the smallest value x such that F(x) >= p, where F is the distribution 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

Extends

Class "DiscreteDistribution", directly.
Class "UnivariateDistribution", by class "DiscreteDistribution".
Class "Distribution", by class "DiscreteDistribution".

Methods

initialize
signature(.Object = "Nbinom"): initialize method
prob
signature(object = "Nbinom"): returns the slot prob of the parameter of the distribution
prob<-
signature(object = "Nbinom"): modifies the slot prob of the parameter of the distribution
size
signature(object = "Nbinom"): returns the slot size of the parameter of the distribution
size<-
signature(object = "Nbinom"): modifies the slot size of the parameter of the distribution
+
signature(e1 = "Nbinom", e2 = "Nbinom"): For the negative binomial distribution we use its closedness under convolutions.

Note

Working with a computer, we use a finite interval as support which carries at least mass 1-getdistrOption("TruncQuantile").

Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de

See Also

NbinomParameter-class Geom-class DiscreteDistribution-class Naturals-class rnbinom

Examples

N <- Nbinom(prob = 0.5, size = 1) # N is a binomial distribution with prob=0.5 and size=1.
r(N)(1) # one random number generated from this distribution, e.g. 3
d(N)(1) # Density of this distribution is  0.25 for x=1.
p(N)(0.4) # Probability that x<0.4 is 0.5.
q(N)(.1) # x=0 is the smallest value x such that p(B)(x)>=0.1.
size(N) # size of this distribution is 1.
size(N) <- 2 # size of this distribution is now 2.

[Package distr version 2.1.1 Index]