The Name "error Function"
The error function is used in measurement theory (using probability and statistics), and although its use in other branches of mathematics has nothing to do with the characterization of measurement errors, the name has stuck.
The error function is related to the cumulative distribution, the integral of the standard normal distribution (the "bell curve"), by
The error function, evaluated at for positive x values, gives the probability that a measurement, under the influence of normally distributed errors with standard deviation, has a distance less than x from the mean value. This function is used in statistics to predict behavior of any sample with respect to the population mean. This usage is similar to the Q-function, which in fact can be written in terms of the error function.
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Famous quotes containing the words the name, error and/or function:
“Do not ask the name of the person who seeks a bed for the night. He who is reluctant to give his name is the one who most needs shelter.”
—Victor Hugo (1802–1885)
“I have often been reproached with the aridity of my genius; a deficiency of imagination has been imputed to me as a crime; and the Pyrrhonism of my opinions has at all times rendered me notorious. Indeed, a strong relish for physical philosophy has, I fear, tinctured my mind with a very common error of this age—I mean the habit of referring occurrences, even the least susceptible of such reference, to the principles of that science.”
—Edgar Allan Poe (1809–1849)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)