R: Class "Nbinom"

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

`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.

### 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@uni-oldenburg.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.
    ## 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.

[Package distr version 2.8.0 Index]