## Empirical CDF

The *empirical distribution function* of a sample,
*F*_{n}(*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.