Gaussian Distribution Function

[William_Horrocks]

Hello! I’m looking for the exact function that is used when generating random numbers using the Gaus(mean, sigma) function in the TRandom class. I’ve done some digging but I can’t find it. If anyone can help me find the function that is used that would be great! Thanks

[Wile_E_Coyote]

See: TRandom::Gaus -> TRandom::Gaus
Note however that, by default, ROOT will internally use: TRandom3::Rndm

[William_Horrocks]

Sorry I should’ve specified, I meant the mathematical function used as the Gaussian distribution function to generate the numbers with, not the function that is called. Thank you for your response though!

[ksmith]

@Wile_E_Coyote posted the link to the implementation. If you want more information about the algorithm, simply read the documentation for TRandom::Gaus:

Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigma.

Uses the Acceptance-complement ratio from W. Hoermann and G. Derflinger This is one of the fastest existing method for generating normal random variables. It is a factor 2/3 faster than the polar (Box-Muller) method used in the previous version of TRandom::Gaus. The speed is comparable to the Ziggurat method (from Marsaglia) implemented for example in GSL and available in the MathMore library.

REFERENCE: - W. Hoermann and G. Derflinger (1990): The ACR Method for generating normal random variables, OR Spektrum 12 (1990), 181-185.

Implementation taken from UNURAN (c) 2000 W. Hoermann & J. Leydold, Institut f. Statistik, WU Wien

[William_Horrocks]

Thank you! I found it.