I came across the table for use with the specialised K-S test and it said that the critical values were calculated using monte carlo calculations using 1000 or more samples for each value of N (sample size). I'm trying to understand how this was done. can anyone help me understand this. This is what i think;
Let the Lilliefors test statistic be and where is the cumulative normal distr. function, F is the empirical c.d.f for the sample , is the e.c.d.f of the sample with .
to simulate the null distribution of the lilliefors test statistic (D) i need to;
1) generate a sample of size n from the standard normal distribution N(0,1)
2) for the sample calculate
3)Do 1) and 2) 1,000 times
4)the distribution of the N values then approximates the null distribution of D
But were do i go on from here to calculate the right tail of this null distribution?