1 DistributionFitTest
“For a test for goodness of fit, a cutoff [Alpha] is chosen such that
Subscript[H, 0] is rejected only if p<[Alpha]. The value of [Alpha]
used for the “TestConclusion” and “ShortTestConclusion” properties is
controlled by the SignificanceLevel option. By default, [Alpha] is set
to 0.05.”
Is default assumption that it is a distribution with known parameters"
For instance, is p-value for Kolmogorov-Smirnov test calculated using
Kolmogorov distribution?
2 DistributionFitTest
"With the setting Method->“MonteCarlo”, k datasets of the same length as
the input Subscript[s, i] are generated under Subscript[H, 0] using the
fitted distribution. The EmpiricalDistribution from
DistributionFitTest[Subscript[s, i],dist,{"TestStatistic",test}]
is then
used to estimate the p-value."
For KS test is p-value a percentage of variates whose KS statistic
vis-a-vis fitted distribution is larger than KS statistic of data?
3 EstimatedDistribution
“Perform goodness-of-fit tests with null distribution dist:”
This returns p-values for various statistical tests. How are those
p-values calculated? Since it is a distribution with estimated
parameters, shouldn’t they be calculated using Monte Carlo? For instance,
Kolmogorov distribution should not be used for KS test.