# Beta-class

0th

Percentile

##### Class "Beta"

The Beta distribution with parameters shape1 $= a$ and shape2 $= b$ has density $$f(x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}{x}^{a} {(1-x)}^{b}$$ for $a > 0$, $b > 0$ and $0 \le x \le 1$ where the boundary values at $x=0$ or $x=1$ are defined as by continuity (as limits).

Keywords
distribution
##### Note

The non-central Beta distribution is defined (Johnson et al, 1995, pp. 502) as the distribution of $X/(X+Y)$ where $X \sim \chi^2_{2a}(\lambda)$ and $Y \sim \chi^2_{2b}$. C.f. rbeta

For R Version <2.3.0< code=""> 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.

##### Extends

Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

##### concept

• absolutely continuous distribution
• Beta distribution
• S4 distribution class
• generating function

BetaParameter-class AbscontDistribution-class Reals-class rbeta

##### Aliases
• Beta-class
• Beta
• initialize,Beta-method
##### 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...
Documentation reproduced from package distr, version 2.2.3, License: LGPL-3

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