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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:
  1. If
    min(p,q)
    > 1, use Cheng algorithm. For details, see [Cheng78].
  2. If
    max(p,q)
    < 1, apply a composition of two algorithms:
    1. If
      q + K*P2 + C ≤ 0
      , where
      K
      = 0.852...,
      C
      = - 0.956..., use Jöhnk algorithm. For details, see [Jöhnk64].
    2. Otherwise, use Atkinson switching algorithm. For details, see [Atkin79].
  3. If
    min(p,q)
    < 1 and
    max(p,q)
    > 1, use the switching algorithm of Atkinson to generate random numbers. For details, see [Atkin79].
  4. If
    p
    = 1 or
    q
    = 1, use the inverse transformation method.
  5. 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)

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804