Contents

# 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

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Notice revision #20110804