Formulas are given for computing the inverse of the error function to at least 18 significant decimal digits for all possible arguments up to 1-10-300 in magnitude. A formula which yields erf (x) to at least 22 decimal places for lxi ? 57r/2 is also developed. 1. Introduction. In statistical work, many types of probability integrals or sums are approximated by functions which involve the normal probability integral or its inverse. Examples where the inverse is used in the asymptotic expansions of x2 distributions can be found in the first four references which are given at the end of this report. J. R. Philip (5) notes that the solution of a one-dimensional concentra- tion-dependent diffusion equation can be obtained with the aid of the inverse error function, and also suggests some formulas which are useful for computation. Formulas for the direct computation of the inverse error function have also been discussed by L. Carlitz (6). Moreover, a computer program which obtains the in-
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Cecil Hastings,et al.
Approximations for digital computers
,
1955
.
[2]
Henry C. Thacher,et al.
Conversion of a power to a series of Chebyshev polynomials
,
1964,
CACM.
[3]
John Wishart.
χ2 PROBABILITIES FOR LARGE NUMBERS OF DEGREES OF FREEDOM
,
1956
.
[4]
E. Cornish,et al.
The Percentile Points of Distributions Having Known Cumulants
,
1960
.
[5]
Henry Goldberg,et al.
Approximate Formulas for the Percentage Points and Normalization of $t$ and $x^2$
,
1946
.
[6]
E. Paulson,et al.
An Approximate Normalization of the Analysis of Variance Distribution
,
1942
.
[7]
L. Carlitz,et al.
The inverse of the error function
,
1963
.
[8]
Jr Phllip,et al.
The Function Inverfc
,
1960
.