Generate Beta-Distributed Random Values by Shape

Generates beta-distributed random values using predefined distributional shapes and transforms them to a specified interval.

Usage

rBetaShape(
  n,
  shape = c("norm", "left", "right", "unif", "u", "j", "inv-j"),
  bounds = c(0, 1)
)

Arguments

n

non-negative integer giving the number of values to generate.

shape

distributional shape: either one of the predefined names listed under Details, or a numeric vector of length 2 giving shape1 and shape2 directly.

bounds

numeric vector containing the lower and upper bound.

Value

a numeric vector of length n with values within bounds.

Details

The following predefined shapes and beta parameters are available:

Shape	shape1	shape2	Description
"norm"	5.0	5.0	symmetric and bell-shaped
"left"	5.0	2.0	left-skewed with values concentrated near the upper bound
"right"	2.0	5.0	right-skewed with values concentrated near the lower bound
"unif"	1.0	1.0	uniform
"u"	0.5	0.5	U-shaped with values concentrated near both bounds
"j"	2.0	0.5	J-shaped with values concentrated near the upper bound
"inv-j"	0.5	2.0	inverse J-shaped with values concentrated near the lower bound

Note that "left" and "right" name the direction of the skew, i.e. of the long tail, so "right" places the bulk of the values near the lower bound. This is the standard convention, but it is the opposite of what the names suggest at first reading - and unrelated to the meaning of "left"/"right" in the sides argument of the interval functions, where they name the side carrying the finite bound.

The "norm" shape is symmetric and bell-shaped but is not a normal distribution. Unlike the normal distribution, all generated values are bounded.

Values from the standard beta distribution on the interval \([0,1]\) are transformed to the interval specified by bounds as

$$a + (b-a)X$$

where \(a\) and \(b\) are the lower and upper bounds, respectively.

Random number generation

The values are drawn with rbeta() and therefore depend on the state of R's global random number generator. No seed is set internally; call set.seed() beforehand, or wrap the call in withSeed(), for reproducible results.

See also

rbeta(), runif()

Other random.numbers: rSum21()

Examples

set.seed(42)

x <- rBetaShape(
  1000,
  shape = "right",
  bounds = c(10, 90)
)

summary(x)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   10.24   22.48   30.91   32.45   40.47   81.73 
range(x)
#> [1] 10.23887 81.73250

# shape parameters can also be given directly
rBetaShape(5, shape = c(3, 1.5), bounds = c(0, 100))
#> [1] 71.50221 70.35936 69.16962 61.70411 19.40427