Empirical distribution function

Summary

The empirical distribution function of a sample is the cumulative distribution function of the distribution that puts mass $1/n$ on each observation. At each point $t$ it gives the fraction of observations that are at most $t$. It estimates the true distribution function without any parametric assumption, and for an i.i.d. sample the Glivenko–Cantelli theorem shows that it converges to it uniformly, almost surely. Goodness-of-fit tests such as the Kolmogorov–Smirnov test compare it with a hypothesised distribution function.