The empirical distribution function provides an example of empirical measures. For real-valued iid random variables it is given by
In this case, empirical measures are indexed by a class It has been shown that is a uniform Glivenko–Cantelli class, in particular,
with probability 1.
Read more about this topic: Empirical Measure
Famous quotes containing the words empirical, distribution and/or function:
“To develop an empiricist account of science is to depict it as involving a search for truth only about the empirical world, about what is actual and observable.... It must involve throughout a resolute rejection of the demand for an explanation of the regularities in the observable course of nature, by means of truths concerning a reality beyond what is actual and observable, as a demand which plays no role in the scientific enterprise.”
—Bas Van Fraassen (b. 1941)
“The man who pretends that the distribution of income in this country reflects the distribution of ability or character is an ignoramus. The man who says that it could by any possible political device be made to do so is an unpractical visionary. But the man who says that it ought to do so is something worse than an ignoramous and more disastrous than a visionary: he is, in the profoundest Scriptural sense of the word, a fool.”
—George Bernard Shaw (1856–1950)
“My function in life is not to be a politician in Parliament: it is to get something done.”
—Bernadette Devlin (b. 1947)