Nbinom-class
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 instantiationr
Object of class
"function"
: generates random numbers (calls functionrnbinom
)d
Object of class
"function"
: density function (calls functiondnbinom
)p
Object of class
"function"
: cumulative function (calls functionpnbinom
)q
Object of class
"function"
: inverse of the cumulative function (calls functionqnbinom
). 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 slotprob
of the parameter of the distribution- prob<-
signature(object = "Nbinom")
: modifies the slotprob
of the parameter of the distribution- size
signature(object = "Nbinom")
: returns the slotsize
of the parameter of the distribution- size<-
signature(object = "Nbinom")
: modifies the slotsize
of the parameter of the distribution- +
signature(e1 = "Nbinom", e2 = "Nbinom")
: For the negative binomial distribution we use its closedness under convolutions.
See Also
NbinomParameter-class
Geom-class
DiscreteDistribution-class
Naturals-class
rnbinom
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.
# }