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 error and/or function:
“There exists a black kingdom which the eyes of man avoid because its landscape fails signally to flatter them. This darkness, which he imagines he can dispense with in describing the light, is error with its unknown characteristics.... Error is certainty’s constant companion. Error is the corollary of evidence. And anything said about truth may equally well be said about error: the delusion will be no greater.”
—Louis Aragon (1897–1982)
“To look backward for a while is to refresh the eye, to restore it, and to render it the more fit for its prime function of looking forward.”
—Margaret Fairless Barber (1869–1901)