# Geom-class

##### Class "Geom"

The geometric distribution with `prob`

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

```
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.
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
```

*Documentation reproduced from package distr, version 2.6, License: LGPL-3*