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Read Paper A handy approximation for the error function and its inverse Sergei Winitzki February 6, 2008 The error function x 2 Z 2 erf x ≡ √ e−x dx (1) …

All of these approximations are valid for x ≥ 0. ... an approximation for the inverse error function:.

[5] lists 3D rational approximations, and [6] contains 7S rational minimax approximations to inverf x and inverfc x. The most accurate set of approximations is ...

The inverse error function erfinv is a standard component of mathemat- ical libraries, and particularly useful in statistical applications for convert-.

Finite Series Approximation ... While the inverse error function is defined by an infinite series expansion, the obvious question becomes how many terms does one ...

For p < 0.5 the inverse erf function is reasonably smooth and the approximation: x = p(p + 10)(Y + R(p)). Gives a good result for a constant Y, ...

Error function, function approximation, spline approximation, ... There are many applications where the inverse error function is required ...

In a recent installment [1], we discussed and compared some useful approximations to the so-called “error functions” re- lated to the Gaussian random variable, ...

01.12.2014 · Looking at the graph of the inverse error function we observe that it is highly non-linear and is therefore difficult to approximate with a polynomial.

I want to approximate the inverse functions erf−1 and erfc−1 for very small values of x. I know that erf∼f(x)= ...

In the following, log() denotes the natural logarithm, R() denotes a rational approximation, and P() denotes a polynomial approximation. A. J. ...

This function is suitable because it is similar to erf (xi). Furthermore, the inverse can easily be determined: >. inverse:= (1/a)*arctanh (xi); (2.2) Note that the Area Tangent, artanh (...), is indicated as arctanh (...) in MAPLE. The best approximation by the hyperbolic tangent is guaranteed by an optimal parameter a which minimizes the L ...

approximation for the error function which is not directly related to those given previously. This new approximation has at least three advantages: it is more ...