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Deadstar · #4 July 3rd, 2009, 04:53 AM

Hmm I'm still not totally clear on this... Let me put down whats in the textbook. Its to do with the Kolmogorov-Smirnov distribution.

I'm testing the hypothesis that a sample of n independent observations comes from a specified continuous distribution.
...Let $F_0(x)$ be the distribution function from which, according to the hypothesis to be tested, the sample has been taken. We let $x_1, x_2, \ldots , x_n$ denote the order statistics of the sample, and define $t_j = F_0(x_j)$ for $j = 1,2, \ldots , n$ .
Then I have a formula to use.
If the null hypothesis holds $t_1, t_2, \ldots t_n$ are the order statistics of a random sample size n from the uniform distribution on (0,1).

And the first thing I have written down to do (written by my prof)...
Set n to be a fixed amount
Calculate $t_1, t_2, \ldots , t_n$ ~ U(0,1)

note, $F_0(x)$ is not given but i assume thats the empirical distribution function?

So, given this info, how would you calculate the t's for say, n=4?

As I say im quite new to stats and this is all the info I have. If I can calculate the t's I'm sorted for the rest of it.