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.