Re: test of normality

Kolmogorov-Smirnovs one sample test



The * characters * of the * drama * are:

__1__A random sample of size n:
________ u_1, u2, ..., u_n
__2__The empirical distribution function, EDF, defined as F(x_j)=1/j (j=1,2,..,j,...n) where x_j is the jth u value from the lesser to the greater (that is there are j-1 u´s values lesser or equal to u_j).
__3__PHI(z) the normal standard normal function.

The method is based on the comparison between F(x_j) and PHI(z) after the transformation
_______x_j = (u_j – m) / s
where m and s are respectively the sample mean and the sample standard deviation.

Note that F([x_j-1, x_j]) = j / n and the test function is the maximum absolute difference, of the EDF and PHI, noted Dmax

The two quantities A and B are evaluated for all j, F(x_0)=0,
___A_j = |F(x_j – 1/j| and B_j =| F(x_j – 1/ (j-1)| __ the greater one let be Y_j.

The value of the test is:
_______Dmax = sup (all j) Y_j

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