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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