Empirical distribution function

The empirical distribution function is an excellent tool for measuring how faithful the sample is to the probability distribution : where observations are densely packed, this function grows rapidly, ...

In the theory of probability, the Glivenko-Cantelli theorem, named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, determines the asymptotic behaviour of the empirical distribution function as the number of iid observations grows.

The graph below is a plot of the empirical distribution function with a normal cumulative distribution function for 100 normal random numbers. The K-S test is based on the maximum distance between these two curves.

See also: Distribution, Distribution function, Density, Normal distribution, Demon