Notes for Intel® oneAPI Math Kernel Library Vector Statistics

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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*P
      2
       + 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

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.