Random.NextBeta Method

Generate a pseudorandom number from a beta distribution.

public virtual double NextBeta(
double p,
double q
);

Parameters

p: A double which specifies the first beta distribution parameter, $p \gt 0$ .
q: A double which specifies the second beta distribution parameter, $q \gt 0$ .

Return Value

A double which specifies a pseudorandom number from a beta distribution.

Remarks

Method NextBeta generates pseudorandom numbers from a beta distribution with parameters p and q, both of which must be positive. The probability density function is

$f\left( x \right) = \frac{{\Gamma \left( {p + q} \right)}}{{\Gamma \left( p \right)\Gamma \left( q \right)}}x^{p - 1} \left( {1 - x} \right)^{q - 1\,\,\,\,} \,\, for\,0 \le x \le 1$

where $\Gamma (\cdot)$ 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.

The value returned is less than 1.0 and greater than $\varepsilon$ , where $\varepsilon$ is the smallest positive number such that $1.0 - \varepsilon$ is less than 1.0.

Random.NextBeta Method

Parameters

Return Value

Remarks

See Also