Inverse Error Function Wiki
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In other words, Q(x) is the probability that a normal (Gaussian) random variable will obtain a value larger than x standard deviations above the mean. If complementary error function the underlying random variable is y, then the proper argument to the error function calculator tail probability is derived as: x = y − μ σ {\displaystyle x={\frac {y-\mu }{\sigma }}} which expresses error function table the number of standard deviations away from the mean. Other definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also used occasionally.[3] Because erf(inf) of its relation to the cumulative 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 mathematics and physics. Contents 1 Definition and basic properties 2 Values 3 Generalization to high dimensions 4 References Definition and basic properties[edit] Formally, the Q-function is defined as Q (
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x ) = 1 2 π ∫ x ∞ exp ( − u 2 2 ) d u . {\displaystyle Q(x)={\frac {1}{\sqrt {2\pi }}}\int _{x}^{\infty }\exp \left(-{\frac {u^{2}}{2}}\right)\,du.} Thus, Q ( x ) = 1 − Q ( − x ) = 1 − Φ ( x ) , {\displaystyle Q(x)=1-Q(-x)=1-\Phi (x)\,\!,} where Φ ( x ) {\displaystyle \Phi (x)} is the cumulative distribution function of the normal Gaussian distribution. The Q-function can be expressed in terms of the error function, or the complementary error function, as[2] Q ( x ) = 1 2 ( 2 π ∫ x / 2 ∞ exp ( − t 2 ) d t ) = 1 2 − 1 2 erf ( x 2 ) -or- = 1 2 erfc ( x 2 ) . {\displaystyle {\begin{aligned}Q(x)&={\frac {1}{2}}\left({\frac {2}{\sqrt {\pi }}}\int _{x/{\sqrt {2}}}^{\infty }\exp \left(-t^{2}\right)\,dt\right)\\&={\frac {1}{2}}-{\frac {1}{2}}\operatorname {erf} \left({\frac {x}{\sqrt {2}}}\right)~~{\text{ -or-}}\\&={\frac {1}{2}}\operatorname {erfc} \left({\frac {x}{\sqrt {2}}}\right).\end{aligned}}} An alternative form of the Q-function known as Craig's formula, after its discoverer, is expressed as:[4] Q ( x ) =
portal v t e This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion. C This article has been rated as
Erf(1)
C-Class on the quality scale. Mid This article has been rated as Mid-importance inverse error function calculator on the importance scale. WikiProjectMathematics (RatedC-class,Mid-importance) Mathematics portal This article is within the scope of WikiProjectMathematics, a collaborative effort to error function excel improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. Mathematicsrating: CClass https://en.wikipedia.org/wiki/Q-function MidImportance Field: Probability and statistics Contents 1 FUBAR!!! ERROR in the ERROR FUNCTION! 2 Bounded function/s? 3 Non-elementary? 4 Asymptotic expansion 5 Complementary versus invserse 6 Erf is "evidently" odd 7 If limits of error function changes? 8 Subscript? 9 Why? 10 Approximation? 11 On alternate forms of error function for improving article 12 ierfc: Integral of the error function complement 13 confused 14 Integral of a https://en.wikipedia.org/wiki/Talk%3AError_function normal distrubution 15 Limits of the error function 16 Relation to moment generating function for the Rayleigh distribution 17 Part of C99 standard? 18 Inverse erfc? 19 representation through Gamma funciton 20 Some errors in the Gamma function expression of the generalised error functions 21 C-like source for approximation 22 Convolved step? 23 Repeated integration 24 Approximation with elementary functions 25 Graph contradicts formula 26 Double factorial 27 Imaginary and Complex error function 28 "The name 'error function'" FUBAR!!! ERROR in the ERROR FUNCTION![edit] Please have someone competent recreate this page. Your error function table of numerical values is WRONG, which is both shockingly inexcusable and could wreak havoc if people actually use it. You can easily verify it is wrong by checking any standard handbook, e. g. CRC handbook of chemistry and physics, CRC math handbook, Lange's handbook of chemistry. Please fix it, and please permanently bar whomever posted it from contributing to Wikipedia. I realize from what I read here that quality control is anathema, but PLEASE, people really might use this to make important decisions! Andy Cutler 184.78.143.36 (talk) 05:40, 14 June 2010 (UTC) The above is possibly a moron's joke; anyway the values reported in th
Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: http://mathworld.wolfram.com/InverseErf.html Tue Sep 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Special Functions>Erf> Calculus and Analysis>Calculus>Integrals>Definite Integrals> History and Terminology>Wolfram Language Commands> Inverse Erf The inverse http://documents.mx/documents/error-function-wikipedia-the-free-encyclopedia.html erf function is the inverse function of the erf function such that (1) (2) with the first identity holding for and the second for . It is error function implemented in the Wolfram Language as InverseErf[x]. It is an odd function since (3) It has the special values (4) (5) (6) It is apparently not known if (7) (OEIS A069286) can be written in closed form. It satisfies the equation (8) where is the inverse erfc function. It has the derivative (9) inverse error function and its integral is (10) (which follows from the method of Parker 1955). Definite integrals are given by (11) (12) (13) (14) (OEIS A087197 and A114864), where is the Euler-Mascheroni constant and is the natural logarithm of 2. The Maclaurin series of is given by (15) (OEIS A002067 and A007019). Written in simplified form so that the coefficient of is 1, (16) (OEIS A092676 and A092677). The th coefficient of this series can be computed as (17) where is given by the recurrence equation (18) with initial condition . SEE ALSO: Confidence Interval, Erf, Inverse Erfc, Probable Error RELATED WOLFRAM SITES: http://functions.wolfram.com/GammaBetaErf/InverseErf/, http://functions.wolfram.com/GammaBetaErf/InverseErf2/ REFERENCES: Bergeron, F.; Labelle, G.; and Leroux, P. Ch.5 in Combinatorial Species and Tree-Like Structures. Cambridge, England: Cambridge University Press, 1998. Carlitz, L. "The Inverse of the Error Function." Pacific J. Math. 13, 459-470, 1963. Parker, F.D. "Integrals of Inverse Functions." Amer. Math. Monthly 62, 439-440, 1955. Sloane, N.J.A. Sequences A002067/M4458, A007019/M3126, A069286, A087197, A092676,
Internet Investor Relations Law Leadership & Management Lifestyle Marketing Mobile News & Politics Presentations & Public Speaking Real Estate Recruiting & HR Retail Sales Science Self Improvement Services Small Business & Entrepreneurship Social Media Software Spiritual Sports Technology Documents Travel Others HomeDocumentsError function - Wikipedia, the free encyclopedia Error function - Wikipedia, the free encyclopedia Mar 30, 2015 Documents deepak-kumar-rout of 8 ×Close Share Error function - Wikipedia, the free encyclopedia Embed Error function - Wikipedia, the free encyclopedia size(px) 750x600 750x500 600x500 600x400 start on 1 2 3 4 5 6 7 8 Link Report Description Text Error function - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Error_function Error function From Wikipedia, the free encyclopedia In mathematics, the error function (also called the Gauss error function or probability integral[1]) is a special function (non-elementary) of sigmoid shape which occurs in probability, statistics and partial differential equations. It is defined as: The complementary error function, denoted erfc, is defined as Plot of the error function The complex error function, denoted w(x) and also known as the Faddeeva function, is defined as Contents 1 Properties 1.1 Taylor series 1.2 Inverse function 1.3 Asymptotic expansion 2 Approximation with elementary functions 3 Applications 4 Related functions 4.1 Generalized error functions 4.2 Iterated integrals of the complementary error function 5 Implementations 6 Table of values 7 See also 7.1 Related functions 7.1.1 In probability 8 References 9 External links Properties 1 of 8 04-03-2011 11:22 AM Error function - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Error_function The error function is odd: Plots in the complex plane Also, for any complex number z: where is the complex conjugate of z. The integrand ƒ = exp(−z2) and ƒ = erf(z) a