This paper compares a number of approximations used to estimate means and variances of continuous random variables and/or to serve as substitutes for the probability distributions of such variables, ...

A random variable is one whose value is unknown or a function that assigns values to each of an experiment’s outcomes. A random variable can be discrete or continuous.

Previously suggested methods for constructing confidence bands for cumulative distribution functions have been based on the classical Kolmogorov-Smirnov test for an empirical distribution function.