uniform_method::standard
uniform_method::accurate
|
uniform
|
Standard method. Currently there is only one method for these functions. uniform_method::accurate checks for additional s and d data types. For integer data types, it uses d as a BRNG data type (s BRNG data type is used in uniform_method::standard method on GPU). |
gaussian_method::box_muller
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gaussian
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Generates normally distributed random number x thru the pair of uniformly distributed numbers u1 and u2 according to the formula:  |
gaussian_method::box_muller2
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gaussian
|
Generates normally distributed random numbers x1 and x2 thru the pair of uniformly distributed numbers u1 and u2 according to the formulas:   Lognormal distribution: generated normally distributed random numbers x1 and x2 are converted to lognormal distribution. |
gaussian_method::icdf
geometric_method::icdf
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gaussian
geometric
|
Inverse cumulative distribution function (ICDF) method. |
exponential_method::icdf
exponential_method::icdf_accurate
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exponential
|
Inverse cumulative distribution function (ICDF) method. |
weibull_method::icdf
weibull_method::icdf_accurate
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weibull
|
Inverse cumulative distribution function (ICDF) method. |
cauchy_method::icdf
|
cauchy
|
Inverse cumulative distribution function (ICDF) method. |
rayleigh_method::icdf
rayleigh_method::icdf_accurate
|
rayleigh
|
Inverse cumulative distribution function (ICDF) method. |
lognormal_method::icdf
lognormal_method::icdf_accurate
|
lognormal
|
Inverse cumulative distribution function (ICDF) method. |
lognormal_method::box_muller2
lognormal_method::box_muller2_accurate
|
lognormal
|
Normally distributed random numbers x1 and x2 are produced through the pair of uniformly distributed numbers u1 and u2 according to the formulas:   Then x1 and x2 are converted to lognormal distribution. |
gumbel_method::icdf
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gumbel
|
Inverse cumulative distribution function (ICDF) method. |
bernoulli_method::icdf
|
bernoulli
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Inverse cumulative distribution function (ICDF) method. |
gamma_method::marsaglia
gamma_method::marsaglia_accurate
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gamma
|
For α > 1, a gamma distributed random number is generated as a cube of properly scaled normal random number; for 0.6 ≤α < 1, a gamma distributed random number is generated using rejection from Weibull distribution; for α < 0.6, a gamma distributed random number is obtained using transformation of exponential power distribution; for α = 1, gamma distribution is reduced to exponential distribution. |
beta_method::cja
beta_method::cja_accurate
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beta
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Cheng-Johnk-Atkinson method. For min(p, q) > 1, Cheng method is used; for min(p, q) < 1, Johnk method is used, if q + K·p2+ C≤ 0 (K = 0.852..., C=-0.956...) otherwise, Atkinson switching algorithm is used; for max(p, q) < 1, method of Johnk is used; for min(p, q) < 1, max(p, q)> 1, Atkinson switching algorithm is used (CJA stands for Cheng, Johnk, Atkinson); for p = 1or q = 1, inverse cumulative distribution function method is used; for p = 1 and q = 1, beta distribution is reduced to uniform distribution. |
chi_square_method::gamma_based
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chi_square
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(most common): If ν ≥ 17 or ν is odd and 5 ≤ ν ≤ 15, a chi-square distribution is reduced to a Gamma distribution with these parameters: Shape α = ν / 2 Offset a = 0 Scale factor β = 2. The random numbers of the Gamma distribution are generated. |
gaussian_mv_method::box_muller
gaussian_mv_method::box_muller2
gaussian_mv_method::icdf
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gaussian_mv
|
BoxMuller method for multivariate Gaussian distribution. BoxMuller_2 method for multivariate Gaussian distribution. Inverse cumulative distribution function (ICDF) method. |
binomial_method::btpe
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binomial
|
Acceptance/rejection method for ntrial·min(p, 1p) ≥ 30 with decomposition into four regions:
Two parallelograms
Triangle
Left exponential tail
Right exponenetial tail
|
poisson_method::ptpe
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poisson
|
Acceptance/rejection method for λ≥ 27 with decomposition into four regions:
Two parallelograms
Triangle
Left exponential tail
Right exponenetial tail
|
poisson_method::gaussian_icdf_based
poisson_v_method::gaussian_icdf_based
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poisson
poisson_v
|
for λ≥ 1, method based on Poisson inverse CDF approximation by Gaussian inverse CDF; for λ < 1, table lookup method is used. |
hypergeometric_method::h2pe
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hypergeometric
|
Acceptance/rejection method for large mode of distribution with decomposition into three regions:
Rectangular
Left exponential tail
Right exponential tail
|
negative_binomial_method::nbar
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negative_binomial
|
Acceptance/rejection method for:  with decomposition into five regions:
Rectangular
(2) trapezoid
Left exponential tail
Right exponential tail
|
multinomial_method::poisson_icdf_based
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multinomial
|
Multinomial distribution with parameters m, k, and a probability vector p. Random numbers of the multinomial distribution are generated by Poisson Approximation method. |
