# Nbinom-class

0th

Percentile

##### Class "Nbinom"

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

Keywords
distribution
##### Note

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

##### 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.

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

##### Aliases
• Nbinom-class
• Nbinom
• initialize,Nbinom-method
##### Examples
# NOT RUN {
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.
# }

Documentation reproduced from package distr, version 2.8.0, License: LGPL-3

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