distr (version 2.9.7)

Nbinom-class: Class "Nbinom"

Description

The negative binomial distribution with size \(= n\), by default \(=1\), and prob \(= p\), by default \(=0.5\), has density $$ d(x) = \frac{\Gamma(x+n)}{\Gamma(n) x!} p^n (1-p)^x$$ for \(x = 0, 1, 2, \ldots\)

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 \(F(x) \ge p\), 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

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 = "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.

Author

Thomas Stabla ,
Florian Camphausen ,
Peter Ruckdeschel ,
Matthias Kohl

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.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
size(N) # size of this distribution is 1.
size(N) <- 2 # size of this distribution is now 2.