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

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 2.1.3 Index]