Beta-class {distr} | R Documentation |

## Class "Beta"

### Description

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} {(1-x)}^{b-1}%
```

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).

### Ad hoc methods

For R Version `<2.3.0`

ad hoc methods are provided for slots `q`

, `r`

if `ncp!=0`

;
for R Version `>=2.3.0`

the methods from package stats are used.

### Objects from the Class

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

.
This object is a beta 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

`"BetaParameter"`

: the parameter of this distribution (shape1 and shape2), declared at its instantiation`r`

Object of class

`"function"`

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

Object of class

`"function"`

: density function (calls function dbeta)`p`

Object of class

`"function"`

: cumulative function (calls function pbeta)`q`

Object of class

`"function"`

: inverse of the cumulative function (calls function qbeta)`.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 `"AbscontDistribution"`

, directly.

Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.

Class `"Distribution"`

, by class `"AbscontDistribution"`

.

### Methods

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

: initialize method- shape1
`signature(object = "Beta")`

: returns the slot shape1 of the parameter of the distribution- shape1<-
`signature(object = "Beta")`

: modifies the slot shape1 of the parameter of the distribution- shape2
`signature(object = "Beta")`

: returns the slot shape2 of the parameter of the distribution- shape2<-
`signature(object = "Beta")`

: modifies the slot shape2 of the parameter of the distribution`-`

`signature(e1 = "numeric", e2 = "Beta")`

if`ncp(e2)==0`

and`e1 == 1`

, an exact (central)`Beta(shape1 = shape2(e2), shape2 = shape1(e2))`

is returned, else the default method is used; exact

### 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`

### Author(s)

Thomas Stabla statho3@web.de,

Florian Camphausen fcampi@gmx.de,

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,

Matthias Kohl Matthias.Kohl@stamats.de

### 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...
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
```

*distr*version 2.9.3 Index]