Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.
Sign up to join this community
Why the test function in Kolmogorov-Smirnov test takes the supremum of the set of differences, not maximum? When maximum (greatest element) of a set does not exist then supremum may exist, but if greatest element exist then supremum is same as greatest element. I want to know why here greatest element does not exist?
Thanks
Prasenjit
Suppose a difference is an increasing continuous function on open interval and zero everywhere else. Then the maximum will not exist, but supremum will.
