Hi;

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 $\displaystyle D=max_{y \in R}|F(y)-S_{0}(y)|$ and $\displaystyle D^{*}=max_{x \in [0,1]}|F^{*}(x)-x|$ where $\displaystyle S_{0}$ is the cumulative normal distr. function, F is the empirical c.d.f for the sample $\displaystyle y_1,...,y_n$ , $\displaystyle F^*$ is the e.c.d.f of the sample $\displaystyle x_1,...,x_n$ with $\displaystyle x_i=S_{0}(y_i)$.

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 $\displaystyle D^*$

3)Do 1) and 2) 1,000 times

4)the distribution of the N values $\displaystyle D^*$ then approximates the null distribution of D

But were do i go on from here to calculate the right tail of this null distribution?