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I can't find what is the distribution corresponding to the default option in:

DistributionFitTest[data, Automatic, "HypothesisTestData"];

Is it N(0,1), uniform?

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Does this answer your question? – Szabolcs Mar 20 '14 at 15:53

By default DistributionFitTest attempts to test fit against the family of normal distributions. To test if the data is standard normal (i.e. N(0,1)) you would use.

DistributionFitTest[data, NormalDistribution[]]

There are examples that show this to be the case in the Properties & Relations section of the documentation for DistributionFitTest.

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When you have time, could you take a look whether this looks reasonable? I have an actual practical need for this. My distribution looks like a histogram, but it comes from probabilistic bisection (see pages 13-15) and not from counting data points. – Szabolcs May 12 '14 at 20:37
@Szabolcs I don't see anything wrong with your approach. I don't have access to the source so I can't promise that the Infinity is safe across the board. You know the typical caveat about undocumented internals being subject to change. – Andy Ross May 14 '14 at 13:45

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