In statistics, an empirical distribution function (commonly also called an
empirical cumulative distribution function , eCDF) is the distribution
function associated with the empirical measure of a sample. This cumulative
distribution function is a step function that jumps up by 1/ n at each of
the n data points. Its value at any specified value of the measured variable
is the fraction of observations of the measured variable that are less than or
equal to the specified value.
The empirical distribution function is an estimate of the cumulative
distribution function that generated the points in the sample. It converges
with probability 1 to that underlying distribution, according to the
Glivenko–Cantelli theorem.