Class "Nbinom"
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 can be created by calls of the form Nbinom(prob, size).
This object is a negative binomial distribution.
imgObject of class "Naturals": The space of the image of this
distribution has got dimension 1 and the name "Natural Space".
paramObject of class "NbinomParameter": the parameter of this distribution (prob, size),
declared at its instantiation
rObject of class "function": generates random numbers (calls function rnbinom)
dObject of class "function": density function (calls function dnbinom)
pObject of class "function": cumulative function (calls function pnbinom)
qObject 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.
supportObject of class "numeric": a (sorted) vector containing the support of the discrete
density function
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject of class "DistributionSymmetry";
used internally to avoid unnecessary calculations.
Class "DiscreteDistribution", directly.
Class "UnivariateDistribution", by class "DiscreteDistribution".
Class "Distribution", by class "DiscreteDistribution".
signature(.Object = "Nbinom"): initialize method
signature(object = "Nbinom"): returns the slot prob of the parameter of the distribution
signature(object = "Nbinom"): modifies the slot prob of the parameter of the distribution
signature(object = "Nbinom"): returns the slot size of the parameter of the distribution
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.
Working with a computer, we use a finite interval as support which carries at least mass 1-getdistrOption("TruncQuantile").
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
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.
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