Notes for Intel® oneAPI Math Kernel Library Vector Statistics

Developer Reference

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Gamma (VSL_RNG_METHOD_GAMMA_GNORM/ VSL_RNG_METHOD_GAMMA_GNORM_ACCURATE)

Random number generator of the gamma distribution with parameters shape
α
, offset
a
, and scale factor
β
. You can generate any successive random number
γ
α
 of the standard gamma distribution (
a =
 0,
β
 = 1) as follows:
  1. If
    α
     > 1, a gamma distributed random number can be generated as a cube of properly scaled normal random number [Mars2000]. The algorithm is based on the acceptance/rejection method using squeeze technique.
  2. If
    α
     < 1, a gamma distributed random number is generated using two acceptance/rejection based algorithms:
    • If
      α
       < 0.6, a gamma distributed random number is obtained by transformation of exponential power distributed random number [Dev86],
    • Otherwise, rejection method from Weibull distribution is used [Vad77], [Dev86].
When
α
 = 1 gamma distribution is reduced to exponential distribution with parameters
a
,
β
. The random numbers of the exponential distribution are generated using method VSL_RNG_METHOD_EXPONENTIAL_ICDF. The gamma distributed random number
γ
 with parameters
α
,
a
, and
β
 is transformed from
γ
α
 using scale and shift
γ = a + βγ
α
.

Product and Performance Information

1

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