Probability distributions - A-Herzog/Warteschlangensimulator GitHub Wiki

Probability distributions supported in Warteschlangensimulator:

Distribution	Type	Use	Fit	WebApp	Pseudorandom number generation
Arcsine	Continuous	Yes	Yes	Yes	Inversion method
Beta	Continuous	Yes	Yes	Yes	Direct method (Cheng's algorithm)
Bernoulli	Discrete	No	No	Yes	Bisection method
Binomial	Discrete	Yes	Yes	Yes	Summing PDF values
Boltzmann	Discrete	Yes	No	Yes	Summing PDF values
Borel	Discrete	Yes	Yes	Yes	Summing PDF values
Cauchy	Continuous	Yes	No	Yes	Inversion method
Chi	Continuous	Yes	Yes	Yes	Bisection method
Chi2	Continuous	Yes	Yes	Yes	Bisection method
ContinuousBernoulli	Continuous	Yes	No	Yes	Bisection method
Cosine	Continuous	Yes	Yes	Yes	Bisection method
DiscreteUniform	Discrete	Yes	Yes	Yes	Summing PDF values
Empirical	Continuous	Yes	No	No	Summing PDF values
Erlang	Continuous	Yes	Yes	Yes	Bisection method
Exponential	Continuous	Yes	Yes	Yes	Inversion method
F	Continuous	Yes	Yes	Yes	Bisection method
FatigueLife	Continuous	Yes	No	Yes	Bisection method
Frechet	Continuous	Yes	No	Yes	Inversion method
Gamma	Continuous	Yes	Yes	Yes	Direct method
GaussKuzmin	Discrete	No	No	Yes	-
Geometric	Discrete	Yes	Yes	Yes	Summing PDF values
Gumbel	Continuous	Yes	Yes	Yes	Bisection method
HalfCauchy	Continuous	Yes	No	Yes	Inversion method
HalfNormal	Continuous	Yes	Yes	Yes	Bisection method
HyperbolicSecant	Continuous	Yes	Yes	Yes	Inversion method
Hypergeometric	Discrete	Yes	No	Yes	Summing PDF values
InverseGamma	Continuous	Yes	No	Yes	Bisection method
InverseGaussian	Continuous	Yes	Yes	Yes	Direct method
IrwinHall	Continuous	Yes	Yes	Yes	Bisection method
JohnsonSU	Continuous	Yes	No	Yes	Direct method (based on normal distribution)
Kumaraswamy	Continuous	Yes	No	Yes	Inversion method
Laplace	Continuous	Yes	Yes	Yes	Inversion method
Levy	Continuous	Yes	No	Yes	Direct method (based on normal distribution)
Logarithmic	Discrete	Yes	Yes	Yes	Summing PDF values
Logistic	Continuous	Yes	Yes	Yes	Inversion method
LogCauchy	Continuous	Yes	No	Yes	Inversion method
LogGamma	Continuous	Yes	No	Yes	Bisection method
LogLaplace	Continuous	Yes	Yes	Yes	Bisection method
LogLogistic	Continuous	Yes	Yes	Yes	Bisection method
LogNormal	Continuous	Yes	Yes	Yes	Direct method (based on normal distribution)
MaxwellBoltzmann	Continuous	Yes	Yes	Yes	Bisection method
NegativeBinomial	Discrete	Yes	Yes	Yes	Summing PDF values
NegativeHypergeometric	Discrete	Yes	No	Yes	Summing PDF values
Normal	Continuous	Yes	Yes	Yes	Direct method (Polar method)
OnePoint	Discrete	Yes	Yes	No	Inversion method
Pareto	Continuous	Yes	Yes	Yes	Inversion method
Pert	Continuous	Yes	Yes	Yes	Bisection method
Planck	Discrete	Yes	Yes	Yes	Summing PDF values
Poisson	Discrete	Yes	Yes	Yes	Summing PDF values
Power	Continuous	Yes	Yes	Yes	Inversion method
Rademacher	Discrete	Yes	Yes	Yes	Inversion method
Rayleigh	Continuous	Yes	Yes	Yes	Inversion method
Reciprocal	Continuous	Yes	Yes	Yes	Inversion method
SawtoothLeft	Continuous	Yes	Yes	Yes	Inversion method
SawtoothRight	Continuous	Yes	Yes	Yes	Inversion method
Sine	Continuous	Yes	Yes	Yes	Inversion method
StudentT	Continuous	Yes	Yes	Yes	Direct method
Trapezoid	Continuous	Yes	Yes	Yes	Inversion method
Triangular	Continuous	Yes	Yes	Yes	Inversion method
Uniform	Continuous	Yes	Yes	Yes	Inversion method
UQuadratic	Continuous	Yes	Yes	Yes	Inversion method
Weibull	Continuous	Yes	Yes	Yes	Inversion method
WignerSemicircle	Continuous	Yes	Yes	Yes	Bisection method
Zeta	Discrete	Yes	Yes	Yes	Summing PDF values

"Use" and "Fit" refers to Warteschlangensimulator. "WebApp" is the probability distribution viewer web app.

Generating pseudorandom numbers by an inversion method is fast. Using the (fallback) bisection method is slow. Direct methods often contain loops and are therefore slower than inversion methods, but overall mostly quite fast.