# Gamma-class

From distr v1.4
by Peter Ruckdeschel

##### Class "Gamma"

The Gamma 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`

##### Objects from the Class

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

.
This object is a gamma distribution.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### See Also

`GammaParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rgamma`

##### Examples

```
G=Gamma(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 1.4, License: GPL (version 2 or later)*

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