# Beta-class

##### Class "Beta"

The Beta distribution with parameters `shape1`

$= a$ and
`shape2`

$= b$ has density
$$f(x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}{x}^{a} {(1-x)}^{b}$$
for $a > 0$, $b > 0$ and $0 \le x \le 1$
where the boundary values at $x=0$ or $x=1$ are defined as
by continuity (as limits).

- Keywords
- distribution

##### Note

The non-central Beta distribution is defined (Johnson et al, 1995,
pp. 502) as the distribution of $X/(X+Y)$ where
$X \sim \chi^2_{2a}(\lambda)$ and
$Y \sim \chi^2_{2b}$.
C.f. `rbeta`

##### Ad hoc methods

For R Version `<2.3.0< code=""> ad hoc methods are provided for slots `

`q`

, `r`

if `ncp!=0`

;
for R Version `>=2.3.0`

the methods from package

##### Objects from the Class

Objects can be created by calls of the form `Beta(shape1, shape2)`

.
This object is a beta distribution.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### concept

- absolutely continuous distribution
- Beta distribution
- S4 distribution class
- generating function

##### See Also

`BetaParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rbeta`

##### Examples

```
B <- Beta(shape1 = 1, shape2 = 1)
# B is a beta distribution with shape1 = 1 and shape2 = 1.
r(B)(1) # one random number generated from this distribution, e.g. 0.6979795
d(B)(1) # Density of this distribution is 1 for x=1.
p(B)(1) # Probability that x < 1 is 1.
q(B)(.1) # Probability that x < 0.1 is 0.1.
shape1(B) # shape1 of this distribution is 1.
shape1(B) <- 2 # shape1 of this distribution is now 2.
Bn <- Beta(shape1 = 1, shape2 = 3, ncp = 5)
# Bn is a beta distribution with shape1 = 1 and shape2 = 3 and ncp = 5.
B0 <- Bn; ncp(B0) <- 0;
# B0 is just the same beta distribution as Bn but with ncp = 0
q(B0)(0.1) ##
q(Bn)(0.1) ## => from R 2.3.0 on ncp no longer ignored...
```

*Documentation reproduced from package distr, version 2.0.6, License: LGPL-3*