# Gammad-class

From distr v2.6
by Peter Ruckdeschel

##### Class "Gammad"

The Gammad distribution with parameters `shape`

$= a$,
by default `= 1`

, and `scale`

$= s$, by default `= 1`

, has
density
$$
d(x)= \frac{1}{{\sigma}^{\alpha}\Gamma(\alpha)} {x}^{\alpha-1} e^{-x/\sigma}%
$$
for $x > 0$, $a > 0$ and $s > 0$.
The mean and variance are
$E(X) = a*s$ and
$Var(X) = a*s^2$. C.f. `rgamma`

- Keywords
- distribution

##### Objects from the Class

Objects can be created by calls of the form `Gammad(scale, shape)`

.
This object is a gamma distribution.

##### Slots

`img`

- Object of class
`"Reals"`

: The space of the image of this distribution has got dimension 1 and the name "Real Space". `param`

- Object of class
`"GammaParameter"`

: the parameter of this distribution (scale and shape), declared at its instantiation `r`

- Object of class
`"function"`

: generates random numbers (calls function rgamma) `d`

- Object of class
`"function"`

: density function (calls function dgamma) `p`

- Object of class
`"function"`

: cumulative function (calls function pgamma) `q`

- Object of class
`"function"`

: inverse of the cumulative function (calls function qgamma) `.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 `"ExpOrGammaOrChisq"`

, directly.
Class `"AbscontDistribution"`

, by class `"ExpOrGammaOrChisq"`

.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"UnivariateDistribution"`

.

##### Methods

- initialize
`signature(.Object = "Gammad")`

: initialize method- scale
`signature(object = "Gammad")`

: returns the slot`scale`

of the parameter of the distribution- scale<-
`signature(object = "Gammad")`

: modifies the slot`scale`

of the parameter of the distribution- shape
`signature(object = "Gammad")`

: returns the slot`shape`

of the parameter of the distribution- shape<-
`signature(object = "Gammad")`

: modifies the slot`shape`

of the parameter of the distribution- +
`signature(e1 = "Gammad", e2 = "Gammad")`

: For the Gamma distribution we use its closedness under convolutions.- *
`signature(e1 = "Gammad", e2 = "numeric")`

: For the Gamma distribution we use its closedness under positive scaling transformations.

##### See Also

`GammaParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rgamma`

##### Examples

```
G <- Gammad(scale=1,shape=1) # G is a gamma distribution with scale=1 and shape=1.
r(G)(1) # one random number generated from this distribution, e.g. 0.1304441
d(G)(1) # Density of this distribution is 0.3678794 for x=1.
p(G)(1) # Probability that x<1 is 0.6321206.
q(G)(.1) # Probability that x<0.1053605 is 0.1.
scale(G) # scale of this distribution is 1.
scale(G) <- 2 # scale of this distribution is now 2.
```

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

### Community examples

Looks like there are no examples yet.