The geometric distribution with `prob`

\(= p\) has density
$$p(x) = p {(1-p)}^{x}$$
for \(x = 0, 1, 2, \ldots\)

C.f. `rgeom`

Objects can be created by calls of the form `Geom(prob)`

.
This object is a geometric 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), 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.

Class `"DiscreteDistribution"`

, directly.
Class `"Nbinom"`

, directly.
Class `"UnivariateDistribution"`

, by class `"DiscreteDistribution"`

.
Class `"Distribution"`

, by class `"DiscreteDistribution"`

.

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)`

- 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

`Nbinom-class`

`GeomParameter-class`

`DiscreteDistribution-class`

`Naturals-class`

`rgeom`

# 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 # }