# Gammad-class

##### Class "Gammad"

The Gammad distribution with parameters `shape`

\(=\alpha\),
by default `= 1`

, and `scale`

\(=\sigma\), by default `= 1`

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

```
# NOT RUN {
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.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
scale(G) # scale of this distribution is 1.
scale(G) <- 2 # scale of this distribution is now 2.
# }
```

*Documentation reproduced from package distr, version 2.8.0, License: LGPL-3*