8.7 Random Number from Beta Distribution

Rbeta

## function (n, alph, bet) 
## {
##     X1 = Rgamma(n, 1, alph)
##     X2 = Rgamma(n, 1, bet)
##     return(X1/(X1 + X2))
## }
## <bytecode: 0x000001e2a41283e0>
## <environment: namespace:math>

Test script

alph = 1
bet = 2
Rbeta(1, alph, bet)

## [1] 0.7729

Rbeta(2, alph, bet)

## [1] 0.4181 0.1584

x = Rbeta(10000, alph, bet)
summary(x)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.140   0.330   0.385   0.594   1.000

sd(x)

## [1] 0.2807

var(x)

## [1] 0.07878

alph / (alph + bet)

## [1] 0.3333

alph * bet / (alph + bet)^2 / (alph + bet + 1)

## [1] 0.05556