Refutation of claims such as "Pi is less random than we thought"
by George Marsaglia.
An article by Tu and Fischman in a Physics journal
has led to worldwide reports that Pi is less random than we
thought, or that Pi is not the best random number generator,
or that Pi seems good but not the best. A careful examination
of the Tu and Fischman procedure shows that it is needlessly
complicated and can be reduced to study of the average value
of (U2-U1)(U2-U3) for uniform variates U produced by a RNG,
(but not on their distribution).
The authors' method of assigning a letter grade, A+,A,B,C,D,E to
a sample mean, based on its distance from the expected value,
suggests naivety in the extreme.
Application, in the present article, to the first
960 million digits of the expansion of Pi shows that they
perform as well as other RNGs on not only the average for
(U2-U1)(U2-U3), but on the more difficult test for their
distribution, consistent with results previously shown in
this journal that Pi does quite well on far more extensive
and difficult-to-pass tests of randomness.
LSTests of Randomness, Pi, Diehard Tests, Random Number Generators
George Marsaglia, email@example.com
Joseph W. McKean,firstname.lastname@example.org
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