distr (version 1.6)

Beta-class: Class "Beta"

Description

The Beta distribution with parameters shape1 $= a$ and shape2 $= b$ has density $$f(x)=\frac{\mathrm{\Gamma }(a+b)}{\mathrm{\Gamma }(a)\mathrm{\Gamma }(b)}{x}^a{(1-x)}^b$$ 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). C.f. rbeta

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".

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.