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).

C.f. rbeta

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)

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

Author(s)

Thomas Stabla Thomas.Stabla@uni-bayreuth.de,
Florian Camphausen Florian.Camphausen@uni-bayreuth.de,
Peter Ruckdeschel Peter.Ruckdeschel@uni-bayreuth.de,
Matthias Kohl Matthias.Kohl@uni-bayreuth.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.

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