Convergence concepts in probability MOC Empirical cumulative distribution function Given a random sample of independent and identically distributed real random variables with CDF , let count how many of are less than or equal to ; i.e. implying . The empirical cumulative distribution function of is prob and converges almost surely to as , hence it is an estimator of the true CDF. Proof proof By Kolmogorov’s law. develop | en | sembr