An asymptotic expansion for the upper percentage points of the distribution
Author:
Henry E. Fettis
Journal:
Math. Comp. 33 (1979), 10591064
MSC:
Primary 62E20
MathSciNet review:
528059
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Abstract: An asymptotic development is given for estimating the value of the variable for which the distribution assumes a preassigned value , in the region where the quantity satisfies This development generalizes a similar one given by Blair and coauthors [2] for the case . It is also shown how the estimates thus obtained may be used in conjunction with various iterative schemes to give more accurate values.
 [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
(54 #9047), http://dx.doi.org/10.1090/S00255718197604210407
 [3]
Henry
E. Fettis, A stable algorithm for computing the
inverse error function in the “tailend” region, Math. Comp. 28 (1974), 585–587. MR 0341812
(49 #6558), http://dx.doi.org/10.1090/S00255718197403418125
 [4]
W. GANDER, "A machine independent algorithm for computing percentage points of the distribution," Z. Angew. Math. Phys., v. 28, 1977, pp. 11331136.
 [5]
J.
R. Philip, The function inverfc 𝜃, Austral. J. Phys.
13 (1960), 13–20. MR 0118857
(22 #9626)
 [6]
Anthony
Strecok, On the calculation of the inverse of
the error function, Math. Comp. 22 (1968), 144–158. MR 0223070
(36 #6119), http://dx.doi.org/10.1090/S00255718196802230702
 [7]
M. ZYCZKOWSKI, "Potenzieren von verallgemeinerten Potenzreihen mit beliebigen Exponent," Z. Angew. Math. Phys., v. 12, 1961, pp. 572576.
 [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. 827830. MR 0421040 (54:9047)
 [3]
 H. E. FETTIS, "A stable algorithm for computing the inverse error function in the 'tailend' region," Math. Comp., v. 28, 1975, pp. 585587. 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. 11331136.
 [5]
 J. R. PHILIP, "The function inverfc ," Austral. J. Phys., v. 13, 1960, pp. 1320. MR 0118857 (22:9626)
 [6]
 A. J. STRECOK, "On the calculation of the inverse of the error function," Math. Comp., v. 22, 1968, pp. 144158. MR 0223070 (36:6119)
 [7]
 M. ZYCZKOWSKI, "Potenzieren von verallgemeinerten Potenzreihen mit beliebigen Exponent," Z. Angew. Math. Phys., v. 12, 1961, pp. 572576.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905280599
PII:
S 00255718(1979)05280599
Keywords:
Chisquare distribution,
inverse incomplete gamma function,
percentage points,
asymptotic expansion
Article copyright:
© Copyright 1979
American Mathematical Society
