.BG
.FN Beta
.FN dbeta
.FN pbeta
.FN qbeta
.FN rbeta
.TL
Beta Distribution
.CS
dbeta(q, shape1, shape2)
pbeta(q, shape1, shape2)
qbeta(p, shape1, shape2)
rbeta(n, shape1, shape2)
.AG q
vector of quantiles.
Missing values (`NA's) are allowed.
.AG p
vector of probabilities.
Missing values (`NA's) are allowed.
.AG n
sample size.
If `length(n)' is larger than 1, then `length(n)' random values are returned.
.AG shape1
vector of (positive) shape parameters.
.AG shape2
vector of (positive) shape parameters.
.RT
density (`dbeta'),
probability (`pbeta'),
quantile (`qbeta'), or
random sample (`rbeta')
for the standard beta distribution with parameters `shape1' and `shape2'.
.SP
.Tr
The density function is given by
.sp
.EQ
delim $$
f sub { s sub 1 , s sub 2 } ( q ) ~=~
{ GAMMA ( s sub 1 + s sub 2 ) } over { GAMMA ( s sub 1 ) GAMMA ( s sub 2 ) }
q sup { s sub 1 - 1 } ( 1 - q ) sup { s sub 2 - 1 } , ~~~ 0 ~<=~ q ~<=~ 1,
~~ s sub 1 , s sub 2 ~>~ 0,
.EN
.sp
where $s sub 1$ and $s sub 2$ are the `shape1' and `shape2' parameters.
.En
.SE
The function `rbeta' causes creation of the dataset `.Random.seed' if it does
not already exist, otherwise its value is updated.
.EX
rbeta(20,2,3) #sample of 20 with shape parameters 2 and 3
.KW distribution
.EQ
delim off
.EN
.WR
