Class "Beta"
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.
imgObject of class "Reals":
The space of the image of this distribution has got dimension 1 and the name "Real Space".
paramObject of class "BetaParameter":
the parameter of this distribution (shape1 and shape2), declared at its instantiation
rObject of class "function":
generates random numbers (calls function rbeta)
dObject of class "function":
density function (calls function dbeta)
pObject of class "function":
cumulative function (calls function pbeta)
qObject of class "function":
inverse of the cumulative function (calls function qbeta)
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject of class "DistributionSymmetry";
used internally to avoid unnecessary calculations.
Class "AbscontDistribution", directly.
Class "UnivariateDistribution", by class "AbscontDistribution".
Class "Distribution", by class "AbscontDistribution".
signature(.Object = "Beta"):
initialize method
signature(object = "Beta"):
returns the slot shape1 of the parameter of the distribution
signature(object = "Beta"):
modifies the slot shape1 of the parameter of the distribution
signature(object = "Beta"):
returns the slot shape2 of the parameter of the distribution
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
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@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
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... ## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
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