TITLE(Beta @@ The Beta Distribution)
USAGE(
dbeta(x, a, b)
pbeta(q, a, b)
qbeta(p, a, b)
rbeta(n, a, b)
)
ALIAS(dbeta)
ALIAS(pbeta)
ALIAS(qbeta)
ALIAS(rbeta)
ARGUMENTS(
ARG(x,q @@ vector of quantiles.)
ARG(p @@ vector of probabilities.)
ARG(n @@ number of observations to generate.)
ARG(a, b @@ positive parameters of the beta distribution.)
)
VALUE(
These functions provide information about the Beta distribution
with parameters LANG(a) and LANG(b).  LANG(dbeta) gives the density,
LANG(pbeta) the distribution function, LANG(qbeta) the
quantile function and LANG(rbeta) generates random deviates.
PARA
The Beta distribution has density
DEQN(f(x) =
OVER(greekGamma (a + b ) @@ greekGamma (a) greekGamma (b))
SUP(x@@a) SUP((1-x)@@b) @@ Gamma(a+b)/(Gamma(a)Gamma(b))x^(a-1)(1-x)^(b-1))
for EQN(a GT 0),
EQN(b GT 0)
and
EQN(0 LT x LT 1).
)
SEEALSO(
LANG(LINK(beta)) for the beta function, and LANG(LINK(dgamma)) for the
Gamma distribution.
)
EXAMPLES(
x <- seq(0,1, length=21)
dbeta(x, 1, 1)
pbeta(x, 1, 1)
)
KEYWORD(distribution)
