Empirical cumulative distribution function
An empirical cumulative distribution function is a monotonic step function calculated from a sample.
Description
Given a sample of n observations drawn from a population that is distributed according to an unknown cumulative distribution function F(x) (i.e., F(x) = P[X < x]), let 1X<x be an indicator function defined on the set of Xi and an argument x. It equals 1 if Xi is less than x. At a given level x, the indicator function is a Bernoulli distributed random variable with p = F(t).
An estimator for F(t) is calculated as:
It follows that nF̂(x) is a sample statistic following a binomial distribution.