Empirical distribution function

In statistics, the empirical distribution function is the distribution function associated with the empirical measure of the sample. This cumulative distribution function is a step function that jumps up by 1/n at each of the n data points. The empirical distribution function estimates the cumulative distribution function underlying of the points in the sample and converges with probability 1 according to the Glivenko–Cantelli theorem. A number of results exist to quantify the rate of convergence of the empirical distribution function to the underlying cumulative distribution function.