Distributions Template Parameter Method#

Method	Distributions	Math Description
`uniform_method::standard` `uniform_method::accurate`	`uniform(s,d)` `uniform(i)`	Standard method. `uniform_method::standard_accurate` supported for `uniform(s, d)` only.
`gaussian_method::box_muller`	`gaussian`	Generates normally distributed random number x thru the pair of uniformly distributed numbers $u_{1}$ and $u_{2}$ according to the formula: $x = \sqrt{- 2 l n u_{1}} \sin (2 π u_{2})$
`gaussian_method::box_muller2`	`gaussian` `lognormal`	Generates normally distributed random numbers $x_{1}$ and $x_{2}$ thru the pair of uniformly distributed numbers $u_{1}$ and $u_{2}$ according to the formulas: $x_{1} = \sqrt{- 2 l n u_{1}} \sin 2 π u_{2}$ $x_{2} = \sqrt{- 2 l n u_{1}} \cos 2 π u_{2}$
`gaussian_method::icdf`	`gaussian`	Inverse cumulative distribution function (ICDF) method.
`exponential_method::icdf` `exponential_method::icdf_accurate`	`exponential`	Inverse cumulative distribution function (ICDF) method.
`weibull_method::icdf` `weibull_method::icdf_accurate`	`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.
`bernoulli_method::icdf`	`bernoulli`	Inverse cumulative distribution function (ICDF) method.
`geometric_method::icdf`	`geometric`	Inverse cumulative distribution function (ICDF) method.
`gumbel_method::icdf`	`gumbel`	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`	Generated normally distributed random numbers $x_{1}$ and $x_{2}$ by box_muller2 method are converted to lognormal distribution.
`gamma_method::marsaglia` `gamma_method::marsaglia_accurate`	`gamma`	For $α > 1$ , a gamma distributed random number is generated as a cube of properly scaled normal random number; for $0.6 \leq α < 1$ , 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`	`beta`	Cheng-Jonhnk-Atkinson method. For $m i n (p, q) > 1$ , Cheng method is used; for $m i n (p, q) < 1$ , Johnk method is used, if $q + K * p 2 + C \leq 0 (K = 0.852 . . ., C = - 0.956 . . .)$ otherwise, Atkinson switching algorithm is used; for $m a x (p, q) < 1$ , method of Johnk is used; for $m i n (p, q) < 1, m a x (p, q) > 1$ , Atkinson switching algorithm is used (CJA stands for Cheng, Johnk, Atkinson); for $p = 1$ or $q = 1$ , 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`	`chi_square`	(most common): If $ν \geq 17$ or $ν$ is odd and $5 \leq ν \leq 15$ , 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.
`binomial_method::btpe`	`binomial`	Acceptance/rejection method for $n t r i a l * m i n (p, 1 - p) \geq 30$ with decomposition into four regions: two parallelograms, triangle, left exponential tail, right exponential tail.
`poisson_method::ptpe`	`poisson`	Acceptance/rejection method for $λ \geq 27$ with decomposition into four regions: two parallelograms, triangle, left exponential tail, right exponential tail.
`poisson_method::gaussian_icdf_based`	`poisson`	for $λ \geq 1$ , method based on Poisson inverse CDF approximation by Gaussian inverse CDF; for $λ < 1$ , table lookup method is used.
`poisson_v_method::gaussian_icdf_based`	`poisson_v`	for $λ \geq 1$ , method based on Poisson inverse CDF approximation by Gaussian inverse CDF; for $λ < 1$ , table lookup method is used.
`hypergeometric_method::h2pe`	`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`	`negative_binomial`	Acceptance/rejection method for: $\frac{(a - 1) (1 - p)}{p} \geq 100$ with decomposition into five regions: rectangular, 2 trapezoid, left exponential tail, right exponential tail.
`multinomial_method::poisson_icdf_based`	`multinomial`	Multinomial distribution with parameters $m, k$ , and a probability vector $p$ . Random numbers of the multinomial distribution are generated by Poisson Approximation method.
`gaussian_mv_method::box_muller`	`gaussian_mv`	BoxMuller method for gaussian_mv method.
`gaussian_mv_method::box_muller2`	`gaussian_mv`	BoxMuller2 method for gaussian_mv method.
`gaussian_mv_method::icdf`	`gaussian_mv`	Inverse cumulative distribution function (ICDF) method.

Parent topic: Host Distributions