Nbinom-class | R Documentation |
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 can be created by calls of the form Nbinom(prob, size)
.
This object is a negative binomial distribution.
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.
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
NbinomParameter-class
Geom-class
DiscreteDistribution-class
Naturals-class
rnbinom
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.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.