In probability theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables. The precise definition is found below. Empirical measures are relevant to mathematical statistics.
The motivation for studying empirical measures is that it is often impossible to know the true underlying probability measure . We collect observations and compute relative frequencies. We can estimate, or a related distribution function by means of the empirical measure or empirical distribution function, respectively. These are uniformly good estimates under certain conditions. Theorems in the area of empirical processes provide rates of this convergence.
Read more about Empirical Measure: Definition, Empirical Distribution Function
Famous quotes containing the words empirical and/or measure:
“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)
“From whatever you wish to know and measure you must take your leave, at least for a time. Only when you have left the town can you see how high its towers rise above the houses.”
—Friedrich Nietzsche (1844–1900)