An asymptotic expansion for the upper percentage points of the -distribution

Author:
Henry E. Fettis

Journal:
Math. Comp. **33** (1979), 1059-1064

MSC:
Primary 62E20

DOI:
https://doi.org/10.1090/S0025-5718-1979-0528059-9

MathSciNet review:
528059

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Abstract | References | Similar Articles | Additional Information

Abstract: An asymptotic development is given for estimating the value of the variable for which the -distribution

**[1]**M. ABRAMOWITZ & I. STEGUN, Editors,*Handbook of Mathematical Functions, with Formulas, Graphs and Tables*, Dover, New York, 1966.**[2]**J. M. BLAIR, C. A. EDWARDS & J. H. JOHNSON, "Rational Chebyshev approximations for the inverse of the error function,"*Math. Comp.*, v. 30, 1976, pp. 827-830. MR**0421040 (54:9047)****[3]**H. E. FETTIS, "A stable algorithm for computing the inverse error function in the 'tail-end' region,"*Math. Comp.*, v. 28, 1975, pp. 585-587. MR**0341812 (49:6558)****[4]**W. GANDER, "A machine independent algorithm for computing percentage points of the -distribution,"*Z. Angew. Math. Phys.*, v. 28, 1977, pp. 1133-1136.**[5]**J. R. PHILIP, "The function inverfc ,"*Austral. J. Phys.*, v. 13, 1960, pp. 13-20. MR**0118857 (22:9626)****[6]**A. J. STRECOK, "On the calculation of the inverse of the error function,"*Math. Comp.*, v. 22, 1968, pp. 144-158. MR**0223070 (36:6119)****[7]**M. ZYCZKOWSKI, "Potenzieren von verallgemeinerten Potenzreihen mit beliebigen Exponent,"*Z. Angew. Math. Phys.*, v. 12, 1961, pp. 572-576.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0528059-9

Keywords:
Chi-square distribution,
inverse incomplete gamma function,
percentage points,
asymptotic expansion

Article copyright:
© Copyright 1979
American Mathematical Society