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Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z )
Error_function
Mathematical relation assigning a probability event to a cost
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
Loss_function
Probability distribution
Robert (August 7, 2003). "The Q-function". Connexions. Barak, Ohad (April 6, 2006). "Q Function and Error Function" (PDF). Tel Aviv University. Archived
Normal_distribution
Optimization algorithm for artificial neural networks
loss function or "cost function" For classification, this is usually cross-entropy (XC, log loss), while for regression it is usually squared error loss
Backpropagation
Mathematical function having a characteristic S-shaped curve or sigmoid curve
example is the error function, which is related to the cumulative distribution function of a normal distribution; another is the arctan function, which is
Sigmoid_function
Complex complementary error function
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
Faddeeva_function
Statistics function
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
Q-function
Mathematical function
lack elementary antiderivatives; the integral of the Gaussian function is the error function: ∫ exp ( − x 2 ) d x = π 2 erf x + C . {\displaystyle \int
Gaussian_function
Method for estimating new data within known data points
at the point xk. The following error estimate shows that linear interpolation is not very precise. Denote the function which we want to interpolate by
Interpolation
Type of function in mathematics
an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at
Analytic_function
Error function: An integral important for normal random variables. Fresnel integral: related to the error function; used in optics. Dawson function:
List of mathematical functions
List_of_mathematical_functions
Internet error message
death – Fatal system error screen Funky caching – Generation, display and storage of dynamic content Link rot – URLs ceasing to function List of HTTP status
HTTP_404
Effect of variables' uncertainties on the uncertainty of a function based on them
combination of variables in the function. The uncertainty u can be expressed in a number of ways. It may be defined by the absolute error Δx. Uncertainties can
Propagation_of_uncertainty
Function that is holomorphic on the whole complex plane
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
Entire_function
Measure of the error of an estimator
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
Mean_squared_error
Graphical representations of the variability of data
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
Error_bar
Reliable digital data delivery methods on unreliable channels
applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery
Error detection and correction
Error_detection_and_correction
{\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
List of integrals of exponential functions
List_of_integrals_of_exponential_functions
Types of special mathematical functions
\operatorname {erf} } is the error function, and erfc {\displaystyle \operatorname {erfc} } is the complementary error function, erfc ( x ) = 1 − erf
Incomplete_gamma_function
Association of one output to each input
= 1. Another common example is the error function. More generally, many functions, including most special functions, can be defined as solutions of differential
Function_(mathematics)
Extension of the factorial function
integrals thereof, such as the error function. There are many interrelations between these functions and the gamma function; notably, the factor π {\displaystyle
Gamma_function
Integral of the Gaussian function, equal to sqrt(π)
statistical mechanics, to find its partition function. Although no elementary function exists for the error function, as can be proven by the Risch algorithm
Gaussian_integral
Measure of algorithm accuracy
estimates of the generalization error throughout the learning process. In a learning problem, the goal is to develop a function f n ( x → ) {\displaystyle
Generalization_error
Artificial neural network node function
In artificial neural networks, the activation function of a node is a function that calculates the output of the node based on its individual inputs and
Activation_function
Theory of getting acceptably close inexact mathematical calculations
is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. What
Approximation_theory
Loss function used in robust regression
the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification
Huber_loss
Measure of complexity of real-valued functions
{\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
Rademacher_complexity
Concepts from statistical hypothesis testing
Type I error, or a false positive, is the incorrect rejection of a true null hypothesis in statistical hypothesis testing. A type II error, or a false
Type_I_and_type_II_errors
Computer programming concept
(VTA) and substantia nigra (SNc) appear to mimic the error function in the algorithm. The error function reports back the difference between the estimated
Temporal_difference_learning
Mathematical function
_{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
Dawson_function
Special function defined by an integral
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
Fresnel_integral
}}'={\hat {H}}\mathbf {{\hat {x}}_{i}} } that minimize the reprojection error function given by ∑ i d ( x i , x i ^ ) 2 + d ( x i ′ , x i ^ ′ ) 2 {\displaystyle
Reprojection_error
Statistics concept
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
Errors_and_residuals
Control loop feedback mechanism
below the setpoint. The integral function of the controller tends to compensate for error by introducing another error in the positive direction. This
PID_controller
Scheme for controlling errors in data over noisy communication channels
groups of two to eight bits). Formally, an error-correcting code is given by its (injective) encoding function f : Σ ∗ ↪ Δ ∗ {\displaystyle f:\Sigma ^{*}\hookrightarrow
Error_correction_code
Numerical method for solving physical or engineering problems
PDE. The residual is the error caused by the trial functions, and the weight functions are polynomial approximation functions that project the residual
Finite_element_method
Elliptic partial differential equation
Furthermore, the error function approaches 1 extremely quickly as its argument increases; in practice, for r > 3.4σ the relative error is smaller than
Poisson's_equation
Continuous probability distribution
{5}{4}}\right)}}} The Kaniadakis κ-Error function (or κ-Error function) is a one-parameter generalization of the ordinary error function defined as: erf κ ( x
Kaniadakis Gaussian distribution
Kaniadakis_Gaussian_distribution
Special mathematical function defined as sin(x)/x
"Sampling by incomplete cosine expansion of the sinc function: Application to the Voigt/complex error function". Appl. Math. Comput. 258: 425–435. arXiv:1407
Sinc_function
Series of functions in mathematics
compute the zeta function by using a large enough value of N, for instance N > | s | {\displaystyle N>\vert s\vert } . Error function π x e x 2 e r f
Asymptotic_expansion
Probability distribution
dz\right).} Substituting the definition of the Faddeeva function (scaled complex error function) yields for the indefinite integral: 1 π ∫ w ( z ) d z
Voigt_profile
Computer programming error
Compilation error or compile error refers to a state when a compiler fails to compile a piece of computer program source code, either due to errors in the
Compilation_error
Probability density function
{\left|\alpha \right|}{\sqrt {2}}}\right)\right)} , with the error function erf. The parameters of the function (that are usually determined by a fit) are: N {\displaystyle
Crystal_Ball_function
Criterion for integration in terms of elementary functions
example of such a function is e − x 2 , {\displaystyle e^{-x^{2}},} whose antiderivative is (with a multiplier of a constant) the error function, familiar in
Liouville's theorem (differential algebra)
Liouville's_theorem_(differential_algebra)
Statistical error measure
In statistics, mean absolute error (MAE) is a measure of errors between paired observations expressing the same phenomenon. Examples of Y versus X include
Mean_absolute_error
C standard library header file
operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions. Different C standards
C_mathematical_functions
Tasks in machine learning
the error function using data which is independent of that used for training. Various networks are trained by minimization of an appropriate error function
Training, validation, and test data sets
Training,_validation,_and_test_data_sets
Analytic function that does not satisfy a polynomial equation
logarithm and inverse trigonometric functions. All special functions such as the gamma, error, bessel, and Riemann zeta functions are transcendental. Equations
Transcendental_function
JavaScript test framework running on Node.js
for completion. describe('Foo', function(){ describe('#bar()', function() { it('should work without error', function(done) { var foo = new Foo(128); foo
Mocha_(JavaScript_framework)
Probability distribution
}}\right),} where erf is the error function, a standard function in many mathematical software packages. The quantile function (or inverse CDF) is written:
Half-normal_distribution
Error that stops the operating system
Windows, a fatal system error can be deliberately caused from a kernel-mode driver with either the KeBugCheck or KeBugCheckEx function. However, this should
Fatal_system_error
Statistical model for a binary dependent variable
link function: the logistic model uses the logit function (inverse logistic function), while the probit model uses the probit function (inverse error function)
Logistic_regression
Type of mathematical function
logarithmic integral (Li or li) and Fresnel integrals (S and C) the error function, e r f ( x ) = 2 π ∫ 0 x e − t 2 d t {\displaystyle \mathrm {erf}
Elementary_function
Type of activation function
linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function: ReLU ( x ) = x + =
Rectified_linear_unit
Methods of calculating definite integrals
behavior of the approximation error as a function of the number of integrand evaluations. A method that yields a small error for a small number of evaluations
Numerical_integration
Mathematical approximation of a function
gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit
Taylor_series
Set of rules defining correctly structured programs
name of a function or variable with a lower-case letter. Example: var a = 5; console.log(a); // 5 console.log(A); // throws a ReferenceError: A is not
JavaScript_syntax
Functions such that f(–x) equals f(x) or –f(x)
sine sinh , {\displaystyle \sinh ,} The error function erf . {\displaystyle \operatorname {erf} .} If a function is both even and odd, it is equal to 0
Even_and_odd_functions
Elementary functions and their finitely iterated integrals
of well-known functions which are Liouvillian but not elementary are the nonelementary antiderivatives, for example: The error function, e r f ( x ) =
Liouvillian_function
Logical error that can often be found in programming
four. An example of this error can occur in the computational language MATLAB with the linspace() linear interpolation function, whose parameters are (lower
Off-by-one_error
Number of incorrect bits transmitted
synchronization errors. The bit error rate (BER) is the number of bit errors per unit time. The bit error ratio (also BER) is the number of bit errors divided
Bit_error_rate
Probability distribution
{\displaystyle \operatorname {erfi} (z)} is the imaginary error function. The moment generating function is given by M ( t ) = 1 + σ t e 1 2 σ 2 t 2 π 2 [ erf
Rayleigh_distribution
equation. erf – error function. erfc – complementary error function. erfcx – scaled complementary error function. erfi – imaginary error function. etr – exponent
List of mathematical abbreviations
List_of_mathematical_abbreviations
Error-detecting code for detecting data changes
that generates it is occasionally used as a hash function. CRCs are based on the theory of cyclic error-correcting codes. The use of systematic cyclic codes
Cyclic_redundancy_check
Description of limiting behavior of a function
increasingly larger, the approximating function becomes increasingly more accurate, leading to an increasingly smaller relative error. This asymptotic relationship
Asymptotic_analysis
Data used to detect errors in other data
is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the
Checksum
Process of mapping a continuous set to a countable set
value (such as round-off error) is referred to as quantization error, noise or distortion. A device or algorithmic function that performs quantization
Quantization (signal processing)
Quantization_(signal_processing)
Measure of variation in statistics
{erf} } is the error function. The proportion that is less than or equal to a number, x, is given by the cumulative distribution function: Proportion ≤
Standard_deviation
Statistical function that converts a probability to a standard normal score
environments where numerical implementations of the inverse error function are available, the probit function may be obtained as probit ( p ) = 2 erf − 1 (
Probit
Adaptive boosting based classification algorithm
feature of the choice of exponential error function is that the error of the final additive model is the product of the error of each stage, that is, e ∑ m −
AdaBoost
Solution of a confluent hypergeometric equation
integer, this equals 2−aθ−a(x/2) where θ is a Bessel polynomial. The error function can be expressed as e r f ( x ) = 2 π ∫ 0 x e − t 2 d t = 2 x π 1
Confluent hypergeometric function
Confluent_hypergeometric_function
{2}}}\right)\right]} is the corresponding cumulative distribution function (where erf is the error function), and T ( h , a ) = φ ( h ) ∫ 0 a φ ( h x ) 1 + x 2 d
List of integrals of Gaussian functions
List_of_integrals_of_Gaussian_functions
Measure of investment risk
normally have a higher tracking error. Thus the tracking error does not include any risk (return) that is merely a function of the market's movement. In
Tracking_error
Probability distribution
x-\mu }{\sigma {\sqrt {2}}}}\right)} where erfc is the complementary error function. If X ∼ N ( μ , Σ ) {\displaystyle {\boldsymbol {X}}\sim {\mathcal {N}}({\boldsymbol
Log-normal_distribution
Measure of prediction accuracy of a forecast
possible (see section below). Mean absolute percentage error is commonly used as a loss function for regression problems and in model evaluation, because
Mean absolute percentage error
Mean_absolute_percentage_error
Integrals not expressible in closed-form from elementary functions
{1}{\ln x}}} (logarithmic integral) e − x 2 {\displaystyle e^{-x^{2}}} (error function, Gaussian integral) sin ( x 2 ) {\displaystyle \sin(x^{2})} and cos
Nonelementary_integral
Statistical learning theory
increasing real-valued function g : [ 0 , ∞ ) → R {\displaystyle g\colon [0,\infty )\to \mathbb {R} } , and an arbitrary error function E : ( X × R 2 ) n →
Representer_theorem
Type of reservoir computer
synapses that connect the hidden neurons to output neurons. Thus, the error function is quadratic with respect to the parameter vector and can be differentiated
Echo_state_network
Recurrent neural network architecture
In 2006 Graves, Fernandez, Gomez, and Schmidhuber introduced a new error function for LSTM: Connectionist Temporal Classification (CTC) for simultaneous
Long_short-term_memory
Describes the sum of independent normal and exponential random variables
^{2}-x}{{\sqrt {2}}\sigma }}\right),} where erfc is the complementary error function defined as erfc ( x ) = 1 − erf ( x ) = 2 π ∫ x ∞ e − t 2 d t .
Exponentially modified Gaussian distribution
Exponentially_modified_Gaussian_distribution
Mathematical formula involving a given set of operations
functions such as the error function or gamma function to be basic. It is possible to solve the quintic equation if general hypergeometric functions are
Closed-form_expression
Study of Galois symmetry groups of differential fields
function, the error function erf x {\displaystyle \operatorname {erf} x} , familiar in statistics. The indefinite integrals of elementary functions
Differential_Galois_theory
Mathematical function
{\displaystyle \alpha ={\tfrac {1}{2}},1,2} we find: (Section 2 of ) Error function: E 1 2 ( z ) = exp ( z 2 ) erfc ( − z ) . {\displaystyle E_{\frac
Mittag-Leffler_function
Decision, action, or inaction by an aircraft pilot
pilot error. Studies have shown that increased errors in judgement and cognitive function of the brain, along with changes in memory function are a few
Pilot_error
Statistical property
The standard error (SE) of a statistic (usually an estimator of a parameter, like the average or mean) is the standard deviation of its sampling distribution
Standard_error
Mathematical functions having established names and notations
cosine ( cos {\displaystyle \cos } ), exponential function ( exp {\displaystyle \exp } ), and error function ( erf {\displaystyle \operatorname {erf} } or
Special_functions
Computer science concept
Lisp program (assuming the 'add' function exists) that adds 1 and 1. However, (_ 1 1) results in syntax error lexical error: '_' is not valid. The lexer is
Syntax_error
Browser-based graphing calculator
sufficiently high iterations. Other functions like trigonometric and other transcendental functions, as well as the error function, factorial, statistical operations
Desmos
Code that indicates the nature of an error
an error code (or a return code) is a numeric or alphanumeric code that indicates the nature of an error and, when possible, why it occurred. Error codes
Error_code
Surface analytical technique
software. Fitting a curve requires a function usually called fitness function, cost function, fitting error function or figure of merit (FOM). It measures
X-ray_reflectivity
Serial communications protocol
is no error during those steps, the server's responding function code will also be the function code sent from the client. If there is any error during
Modbus
Statistic expressing the amount of random sampling error in a survey's results
The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence
Margin_of_error
Limit of the tangent line at a point that tends to infinity
− x 2 ) , {\displaystyle x\mapsto \exp(-x^{2}),} the error function, and the logistic function. When a linear asymptote is not parallel to the x- or
Asymptote
Study of kind and quantity of error
both forward error analysis and backward error analysis. Forward error analysis involves the analysis of a function z ′ = f ′ ( a 0 , a 1 , … , a n ) {\displaystyle
Error_analysis_(mathematics)
Probability distribution
instance of the hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution
Student's_t-distribution
Integer number that is made available to the parent of a terminated process
failure (Warning, Error, Fatal). In Plan 9's C, exit status is indicated by a string passed to the exits() function, and function main() is type void
Exit_status
Table of probabilities related to the normal distribution
}^{z}e^{-t^{2}/2}\,dt} Φ {\displaystyle \Phi } (z) is related to the error function, or erf(z). Φ ( z ) = 1 2 [ 1 + erf ( z 2 ) ] {\displaystyle \Phi
Standard_normal_table
Quantization error in numerical analysis
computational physics, and simulation, discretization error is the error resulting from the fact that a function of a continuous variable is represented in the
Discretization_error
hypergeometric integral V. N. Faddeeva: Faddeeva function (also known as the complex error function; see error function) C. F. Gauss: Gaussian polynomial, Gaussian
List of eponyms of special functions
List_of_eponyms_of_special_functions
Digital modulation scheme
by noise. The probability density function of having an error of a given size can be modelled by a Gaussian function; the mean value will be the relative
Amplitude-shift_keying
ERROR FUNCTION
ERROR FUNCTION
Girl/Female
Shakespearean
The Comedy of Errors' Adriana's servant.
Male
Swiss
, axe, or, terror.
Boy/Male
Anglo Saxon
Terror.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Error-less
Boy/Male
English American German Latin Scottish
Army commander. Army, weald power. Also can be a, meaning nobleman. Famous bearer: Australian...
Girl/Female
Hindu, Indian
Without Error
Boy/Male
American, Anglo, British, Christian, Danish, English, German, Jamaican, Latin, Scottish
To Wander; Nobleman; Leader; Earl; Wanderer
Boy/Male
Arabic, Hindu, Indian, Muslim, Tamil
Terror; Kings; Royal
Male
English
Scottish surname transferred to forename use, from a place name possibly ERROL means "to wander."Â
Boy/Male
Anglo Saxon
Terror.
Girl/Female
Australian, British, English, Gaelic, Irish
Terror; Lovers
Boy/Male
Anglo Saxon
Terror.
Boy/Male
Hindu
King of terror
Female
Arthurian
, error for Nineve (q.v.).
Male
Swiss
, axe, or, terror.
Boy/Male
Tamil
King of terror
Boy/Male
Anglo Saxon
Terror.
Boy/Male
Christian & English(British/American/Australian)
Wanderering Noble
Boy/Male
Shakespearean
The Comedy of Errors' A merchant.
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, English, French, Indian, Scottish, Teutonic
Maker of Arrows; Arror Featherer
ERROR FUNCTION
ERROR FUNCTION
Boy/Male
Arabic, Muslim, Pakistani
Balance
Boy/Male
Hindu, Indian
Good Person
Boy/Male
Arabic, Muslim
Benefactor
Girl/Female
Muslim/Islamic
Beautiful companion of prophet (S.A.W)
Boy/Male
Biblical American Hebrew Shakespearean
Poor; humble.
Boy/Male
Tamil
Kripanidhi | கரபாநிதி
One with heart full of mercy
Boy/Male
Tamil
Girl/Female
Gujarati, Hindu, Indian, Telugu
Great
Boy/Male
Hindu
Rushikesh
Boy/Male
Polynesian
Little trees.
ERROR FUNCTION
ERROR FUNCTION
ERROR FUNCTION
ERROR FUNCTION
ERROR FUNCTION
n.
The difference between the approximate result and the true result; -- used particularly in the rule of double position.
n.
The difference between an observed value and the true value of a quantity.
n.
The difference between the observed value of a quantity and that which is taken or computed to be the true value; -- sometimes called residual error.
n.
A fault of a player of the side in the field which results in failure to put out a player on the other side, or gives him an unearned base.
n.
One who encourages and propagates error; one who holds to error.
n.
Erroneous thought; mistaken opinion; error.
n.
A departing or deviation from the truth; falsity; false notion; wrong opinion; mistake; misapprehension.
n.
Misguidance; error.
n.
A moral offense; violation of duty; a sin or transgression; iniquity; fault.
n.
A wandering; a roving or irregular course.
n.
An error; a mistake.
n.
An error in pleading.
a.
Full of error; wrong.
n.
Mistake; error; fault.
n.
One who leads into error.
n.
Liability to error.
n.
A mistake in the proceedings of a court of record in matters of law or of fact.
n.
Exemption from error.
n.
A wandering or deviation from the right course or standard; irregularity; mistake; inaccuracy; something made wrong or left wrong; as, an error in writing or in printing; a clerical error.
a.
Liable to error; fallible.