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Computing in Science & Engineering, 2021
Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by Polya.
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Prompted by previous work published in this magazine, in this article we focus on the derivation of global analytical bounds for the error function of a real argument. Using an integral representation of this function, we obtain two simple and accurate lower bounds, which complement a well-known upper bound given long ago by Polya.
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SSRN Electronic Journal, 2008
Measurement error can lead to biased parameter estimates and misleading test results. In cross-sectional asset pricing models (e.g., CAPM, Fama-French, good beta/bad beta), measurement error can easily arise in calculating portfolio betas. A common approach to the errors-in-variables problem is instrumental variables. Econometrically, conditional asset
Huntley Schaller, Lynda Khalaf
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Measurement error can lead to biased parameter estimates and misleading test results. In cross-sectional asset pricing models (e.g., CAPM, Fama-French, good beta/bad beta), measurement error can easily arise in calculating portfolio betas. A common approach to the errors-in-variables problem is instrumental variables. Econometrically, conditional asset
Huntley Schaller, Lynda Khalaf
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SeMA Journal, 2014
After exploring the particular situation of a non-variational elliptic equation, we introduce the formal concept of an error functional as a generalization of the intuitive idea of a non-negative functional whose only possible critical value is zero. The main result we prove is that such an error is a true measure of how far we are from the zero set of
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After exploring the particular situation of a non-variational elliptic equation, we introduce the formal concept of an error functional as a generalization of the intuitive idea of a non-negative functional whose only possible critical value is zero. The main result we prove is that such an error is a true measure of how far we are from the zero set of
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International Journal of Number Theory, 2007
This paper investigates a new special function referred to as the error zeta function. Derived as a fractional generalization of hypergeometric zeta functions, the error zeta function is shown to exhibit many properties analogous to its hypergeometric counterpart, including its intimate connection to Bernoulli numbers. These new properties are treated
ABDUL HASSEN, HIEU D. NGUYEN
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This paper investigates a new special function referred to as the error zeta function. Derived as a fractional generalization of hypergeometric zeta functions, the error zeta function is shown to exhibit many properties analogous to its hypergeometric counterpart, including its intimate connection to Bernoulli numbers. These new properties are treated
ABDUL HASSEN, HIEU D. NGUYEN
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Approximations to Error Functions
IEEE Instrumentation & Measurement Magazine, 2007This paper addresses approximations to error functions and points out three representative approximations, each with its own merits. Cody's approximation is the most computationally intensive of the three, it is not overly so, and there is no arguing over its accuracy.
Stephen Dyer, Justin Dyer
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Statistics & Risk Modeling, 1983
The paper deals with the problem whether approximations to distributions of estimators (e.g., normal approximations or Edgeworth expansions) can be used for obtaining approximations of risks. It is shown that for loss functions with ''diminishing increment'', the relative errors of the approximating risk functions can be computed from the errors of the
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The paper deals with the problem whether approximations to distributions of estimators (e.g., normal approximations or Edgeworth expansions) can be used for obtaining approximations of risks. It is shown that for loss functions with ''diminishing increment'', the relative errors of the approximating risk functions can be computed from the errors of the
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On error backpropagation algorithm using absolute error function
IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028), 2003We propose error backpropagation using the absolute error function as an objective function. The error backpropagation is the most popular learning algorithm for multi-layered neural networks. In the error backpropagation, the square error function is usually used as the objective function. But a square function has a drawback in which it is enormously
K. Taji, T. Miyake, H. Tamura
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A Kuczma-type functional inequality for error and complementary error functions
Aequationes mathematicae, 2014The error, resp. complementary error functions are defined by \[ \text{erf}(x)= {2\over\sqrt{\pi}} \int^x_0 e^{-t^2}\,dt, \] and \(\text{erf}_c(x)= 1-\text{erf}(x)\). Inspired by an interesting functional equation by \textit{M. Kuczma} [Rocz. Nauk.-Dydakt., Pr. Mat. 13, 197--213 (1993; Zbl 0964.39501)], namely \(x+ F(y+G(x))= y+F(x+ G(y))\), the author
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Functional inequalities for the error function
Aequationes mathematicae, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Computation of the Complex Error Function
SIAM Journal on Numerical Analysis, 1994The paper gives an expansion of the error function (normal probability function) for complex values of the argument. The expansion is in terms of rational functions. Asymptotic properties of the coefficients of the expansion are studied and a compact Matlab program is given. A comparison is made with other algorithms from the literature.
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