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

Keywords
distribution
Note

The non-central Beta distribution is defined (Johnson et al, 1995, pp. 502) as the distribution of $X/(X+Y)$ where $X ~ chi^2_2a(lambda)$ and $Y ~ chi^2_2b$. 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 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
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 2.6, License: LGPL-3

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