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)

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@itwm.fraunhofer.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...

[Package distr version 2.0.6 Index]