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Anderson-Darling: Clarify definition via contrasting to the NIST definition.

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NAThompson
2019-10-05 14:15:42 -04:00
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doc/distributions/anderson_darling.qbk
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@@ -134,6 +134,16 @@ AndersonDarlingNormalityTest<double>/16777216 706160246 ns bytes_per_second=
AndersonDarlingNormalityTest<double>_BigO 42.06 N
```
[heading Caveats]
Some authors, including [@https://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm NIST], give the following definition of the Anderson-Darling test statistic:
[$../graphs/alternative_anderson_darling_definition.svg]
This is an approximation to the quadrature sum we use as our definition.
Boost.Math /does not compute this quantity/.
(However, with a sufficiently large amount of data the two definitions seem to agree to two digits, so the importance of making a clear distinction between the two is unclear.)
Our computation of the Anderson-Darling test statistic agrees with Mathematica.
[endsect]
[/section:anderson_darling]

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