The empirical distribution function of a sample,
Fn(y), is the proportion
of observations less than or equal to y.
where n is the number of observations,
and is an indicator
function with value 1 if and with value 0 otherwise.
The Kolmogorov statistic D is a measure
of the discrepancy between the empirical
distribution and the hypothesized distribution.
where F(y) is the hypothesized
cumulative distribution function.
The statistic is the maximum vertical distance
between the two distribution functions.
The Kolmogorov statistic can be used to construct a confidence
band for the unknown distribution function, to test for a
hypothesized completely known distribution, and to test for
a specific family of distributions with unknown parameters.
If you select a Weight variable,
the weighted empirical distribution function is the proportion
of observation weights for observations less than or equal to y.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.