Converting a Uniform Distribution to a Normal Distribution

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There are plenty of methods:

  • Do not use Box Muller. Especially if you draw many gaussian numbers. Box Muller yields a result which is clamped between -6 and 6 (assuming double precision. Things worsen with floats.). And it is really less efficient than other available methods.
  • Ziggurat is fine, but needs a table lookup (and some platform-specific tweaking due to cache size issues)
  • Ratio-of-uniforms is my favorite, only a few addition/multiplications and a log 1/50th of the time (eg. look there).
  • Inverting the CDF is efficient (and overlooked, why ?), you have fast implementations of it available if you search google. It is mandatory for Quasi-Random numbers.

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