## 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*.

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