In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function e r f : C → C {\displaystyle \mathrm {erf}...

optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one...

Robert (August 7, 2003). "The Q-function". Connexions. Barak, Ohad (April 6, 2006). "Q Function and Error Function" (PDF). Tel Aviv University. Archived...

example is the error function, which is related to the cumulative distribution function of a normal distribution; another is the arctan function, which is...

loss function or "cost function" For classification, this is usually cross-entropy (XC, log loss), while for regression it is usually squared error loss...

distribution function of the normal distribution, the Q-function can also be expressed in terms of the error function, which is an important function in applied...

{\text{ for }}a>0,\ a\neq 1} In the following formulas, erf is the error function and Ei is the exponential integral. ∫ e c x ln ⁡ x d x = 1 c ( e c x...

propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them...

squares of the errors—that is, the average squared difference between the estimated values and the true value. MSE is a risk function, corresponding to...

_{0}^{\infty }e^{-t^{2}/4}\,\sin(xt)\,dt.} It is closely related to the error function erf, as D + ( x ) = π 2 e − x 2 erfi ⁡ ( x ) = − i π 2 e − x 2 erf ⁡...

are statistically significant. Error bars can also suggest goodness of fit of a given function, i.e., how well the function describes the data. Scientific...

from interpolation error and give better performance in calculation process. This table gives some values of an unknown function f ( x ) {\displaystyle...

applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery...

The Faddeeva function or Kramp function is a scaled complex complementary error function, w ( z ) := e − z 2 erfc ⁡ ( − i z ) = erfcx ⁡ ( − i z ) = e...

lack elementary antiderivatives; the integral of the Gaussian function is the error function: ∫ e − x 2 d x = π 2 erf ⁡ x + C . {\displaystyle \int e^{-x^{2}}\...

is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. What...

\operatorname {erf} } is the error function, and erfc {\displaystyle \operatorname {erfc} } is the complementary error function, erfc ⁡ ( x ) = 1 − erf ⁡...

statistical mechanics, to find its partition function. Although no elementary function exists for the error function, as can be proven by the Risch algorithm...

Error function: An integral important for normal random variables. Fresnel integral: related to the error function; used in optics. Dawson function:...

In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element...

(VTA) and substantia nigra (SNc) appear to mimic the error function in the algorithm. The error function reports back the difference between the estimated...

integrals thereof, such as the error function. There are many interrelations between these functions and the gamma function; notably, the factor π {\displaystyle...

well as derivatives and integrals of entire functions such as the error function. If an entire function f ( z ) {\displaystyle f(z)} has a root at w...

= 1. Another common example is the error function. More generally, many functions, including most special functions, can be defined as solutions of differential...

the probit function is available as norm.s.inv(p). In computing environments where numerical implementations of the inverse error function are available...

{\displaystyle h} represents a binary classifier, the error function is a 0–1 loss function, i.e. the error function f h {\displaystyle f_{h}} returns 0 if h {\displaystyle...

functions F(x) and G(x) are transcendental functions named after Augustin-Jean Fresnel that are used in optics and are closely related to the error function...

estimates of the generalization error throughout the learning process. In a learning problem, the goal is to develop a function f n ( x → ) {\displaystyle...

used to compute the zeta function by using a large enough value of N, for instance N > | s | {\displaystyle N>|s|} . Error function π x e x 2 e r f c ( x...

The activation function of a node in an artificial neural network is a function that calculates the output of the node based on its individual inputs and...