Beta-class

0th

Percentile

Class "Beta"

The Beta distribution with parameters shape1 \(= a\) and shape2 \(= b\) has density $$f(x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}{x}^{a-1} {(1-x)}^{b-1}% $$ 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).

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 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

See Also

BetaParameter-class AbscontDistribution-class Reals-class rbeta

Aliases
  • Beta-class
  • Beta
  • initialize,Beta-method
Examples
# NOT RUN {
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(.)(.)
# }
Documentation reproduced from package distr, version 2.7.0, License: LGPL-3

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