Geom-class
Class "Geom"
The geometric distribution with prob
\(= p\) has density
$$p(x) = p {(1-p)}^{x}$$
for \(x = 0, 1, 2, \ldots\)
C.f. rgeom
- 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 Geom(prob)
.
This object is a geometric 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), declared at its instantiation (size=1)r
Object of class
"function"
: generates random numbers (calls function rgeom)d
Object of class
"function"
: density function (calls function dgeom)p
Object of class
"function"
: cumulative function (calls function pgeom)q
Object of class
"function"
: inverse of the cumulative function (calls function qgeom). 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 "Nbinom"
, directly.
Class "UnivariateDistribution"
, by class "DiscreteDistribution"
.
Class "Distribution"
, by class "DiscreteDistribution"
.
Contains-Relations
By means of a contains
argument in the class declaration, R ``knows''
that a distribution object obj
of class "Geom"
also is a
negative Binomial distribution with parameters size = 1, prob = prob(obj)
Methods
- initialize
signature(.Object = "Geom")
: initialize method- prob
signature(object = "Geom")
: returns the slot prob of the parameter of the distribution- prob<-
signature(object = "Geom")
: modifies the slot prob of the parameter of the distribution
See Also
Nbinom-class
GeomParameter-class
DiscreteDistribution-class
Naturals-class
rgeom
Examples
# NOT RUN {
G <- Geom(prob = 0.5) # G is a geometric distribution with prob = 0.5.
r(G)(1) # one random number generated from this distribution, e.g. 0
d(G)(1) # Density of this distribution is 0.25 for x = 1.
p(G)(1) # Probability that x<1 is 0.75.
q(G)(.1) # x = 0 is the smallest value x such that p(G)(x) >= 0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
prob(G) # prob of this distribution is 0.5.
prob(G) <- 0.6 # prob of this distribution is now 0.6.
as(G,"Nbinom")
G+G+G
# }