R: Class "Beta"

Beta-class {distr} | R Documentation

## Class "Beta"

### Description

The Beta distribution with parameters `shape1` = a and `shape2` = b has density

Gamma(a+b)/(Gamma(a)Gamma(b))x^(a-1)(1-x)^(b-1)

for a > 0, b > 0 and 0 <= x <= 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 ~ chi^2_2a(lambda) and Y ~ 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(.)(.)

[Package distr version 2.8.0 Index]