Generates pseudorandom numbers from a beta distribution.

Routine RNBET generates pseudorandom numbers from a beta distribution with parameters PIN and QIN, both of which must be positive. With p = PIN and q = QIN, the probability density function is

where Γ(⋅) is the gamma function.

The algorithm used depends on the values of p and q. Except for the trivial cases of p = 1 or q = 1, in which the inverse CDF method is used, all of the methods use acceptance/rejection. If p and q are both less than 1, the method of Johnk (1964) is used; if either p or q is less than 1 and the other is greater than 1, the method of Atkinson (1979) is used; if both p and q are greater than 1, algorithm BB of Cheng (1978), which requires very little setup time, is used if NR is less than 4; and algorithm B4PE of Schmeiser and Babu (1980) is used if NR is greater than or equal to 4. Note that for p and q both greater than 1, calling RNBET in a loop getting less than 4 variates on each call will not yield the same set of deviates as calling RNBET once and getting all the deviates at once.

The values returned in R are less than 1.0 and greater than ɛ, where ɛ is the smallest positive number such that 1.0 ‑ ɛ is less than 1.0.

In this example, RNBET is used to generate five pseudorandom beta (3, 2) variates.