Beta (VSL_RNG_METHOD_BETA_CJA/ VSL_RNG_METHOD_BETA_CJA_ACCURATE)
Random number generator of the beta distribution with two shape parameters p and q, offset a, and scale factor β. You can generate any successive random number Θ(p,q) of the standard gamma distribution (a = 0, β = 1) as follows:
If min(p,q) > 1, use Cheng algorithm. For details, see [Cheng78].
If max(p,q) < 1, apply a composition of two algorithms:
If min(p,q) < 1 and max(p,q) > 1, use the switching algorithm of Atkinson to generate random numbers. For details, see [Atkin79].
If p = 1 or q = 1, use the inverse transformation method.
If p = 1 and q = 1, standard beta distribution is reduced to the uniform distribution over the interval (0,1). The random numbers of the uniform distribution are generated using the VSL_RNG_METHOD_UNIFORM_STD method.
The algorithms of Cheng and Atkinson use acceptance/rejection technique. The beta distributed random number γ with the parameters p, q, a, and β is transformed from Θ(p,q) as follows: γ = a + βΘ(p,q)
See Intel® oneAPI Math Kernel Library Vector Statistics Random Number Generator Performance Data for test results summary.
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