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, and J. H. Johnson,*Rational Chebyshev approximations for the inverse of the error function*, Math. Comp.**30**(1976), no. 136, 827–830. MR**0421040**, https://doi.org/10.1090/S0025-5718-1976-0421040-7**[3]**Henry E. Fettis,*A stable algorithm for computing the inverse error function in the “tail-end” region*, Math. Comp.**28**(1974), 585–587. MR**0341812**, https://doi.org/10.1090/S0025-5718-1974-0341812-5**[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 𝜃*, Austral. J. Phys.**13**(1960), 13–20. MR**0118857****[6]**Anthony Strecok,*On the calculation of the inverse of the error function*, Math. Comp.**22**(1968), 144–158. MR**0223070**, https://doi.org/10.1090/S0025-5718-1968-0223070-2**[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