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:
- Ifmin(p,q)> 1, use Cheng algorithm. For details, see [Cheng78].
- Ifmin(p,q)< 1 andmax(p,q)> 1, use the switching algorithm of Atkinson to generate random numbers. For details, see [Atkin79].
- Ifp= 1 orq= 1, use the inverse transformation method.
- Ifp= 1 andq= 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.