Beta-class {distr} | R Documentation |
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).
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 can be created by calls of the form Beta(shape1, shape2)
.
This object is a beta distribution.
img
:"Reals"
:
The space of the image of this distribution has got dimension 1 and the name "Real Space". param
:"BetaParameter"
:
the parameter of this distribution (shape1 and shape2), declared at its instantiation r
:"function"
:
generates random numbers (calls function rbeta)d
:"function"
:
density function (calls function dbeta)p
:"function"
:
cumulative function (calls function pbeta)q
:"function"
:
inverse of the cumulative function (calls function qbeta)
Class "AbscontDistribution"
, directly.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "AbscontDistribution"
.
signature(.Object = "Beta")
:
initialize methodsignature(object = "Beta")
:
returns the slot shape1 of the parameter of the distributionsignature(object = "Beta")
:
modifies the slot shape1 of the parameter of the distributionsignature(object = "Beta")
:
returns the slot shape2 of the parameter of the distributionsignature(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
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
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de
BetaParameter-class
AbscontDistribution-class
Reals-class
rbeta
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...