Adjust some of the [rand.dist] critical values that are too strict
- Most critical values are determined empirically by running each test
51
times with a different PRNG seed and finding the smallest symmetric
interval
around the median that contains 90% of the sample means, variances, etc.
- For the Kolmogorov-Smirnov tests, the alpha=0.1 critical value for
large N
is 1.224/sqrt(N).
- For normally distributed variates, the sample kurtosis is distributed
as
Normal(0, 24/N). For N=1e5, this gives a 90% confidence interval of
0+/-0.0255. For Binomial(40, 0.25), which is approximately normal, the
kurtosis is -0.0167, so the relative 90% CI is large, on the order of
0.0255/0.0167 = 153%. In most cases the distribution of the sample
kurtosis
isn't known analytically, but similarly large relative tolerances can be
expected if the kurtosis is near zero.
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