The Kolmogorov-Smirnov-Test can be used to test if a given sample-distribution equals a reference distribution.

I'm sorry to give you the link to the German wikipedia, but the english article differs and my question simply refers to a formula: here

It states that we need to compute the maximum of these terms:

d_{o,i} = abs(S(x_i)-F_0(x_i))
d_{u,i} = abs(S(x_{i-1}-F_0(x_i))

And then compare max(d_o, d_u) with a critical value.

I do understand that the KS-test compares the CDF of the sample distribution with the CDF of the hypothesized distribution. I can also understand why we compute d_o, as it is the difference between these two CDFs. However, I don't understand what the second term (d_u) is being used for.

Can someone kindly explain this to me?



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