Algorithm 724; Program to calculate F-Percentiles

ABSTRACT

Let 0← p ←1 be given and let F be the cumulative distribution function of the F-Distribution with (M, N,) degrees of freedom. This FORTRAN 77 routine is a complement to [1] where a method was presented to find the inverse of the F-Distribution function, FINV(M, N, P), using a series expansion technique to find the inverse for the Beta Distribution function.

REFERENCES

• 1: Roger W. Abernathy , Robert P. Smith, Applying series expansion to the inverse beta distribution to find percentiles of the F-distribution, ACM Transactions on Mathematical Software (TOMS), v.19 n.4, p.474-480, Dec. 1993 [doi>10.1145/168173.168387]
• 2: CARTER, A. H. 1947. Approximations to percentage points of the z-distribution. Biometrika 34, 352-358.
• 3: GOLDBERG, H., AND LEVINE, H. 1946. Approximate formulas for the student's t-distribution. Biometrika 55, 571 572.
• 4: Cecil Hastings, Approximations for Digital Computers, Princeton University Press, Princeton, NJ, 1955
• 5: HILL, G. W., AND DAVIS, A. W. 1968. Generalized asymptotic expansions of Cornish Fisher type. AMS 39, 1264-1273.
• 6: MAJUMDER, J. L., AND BATTACHARJEE, G.P.1973b. Algorithm AS 64: inverse of the incomplete Beta function ratio. Appl. Stat. 22,411 414.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms, Experimentation, Theory

Keywords:
F-Distribution, Newton's method, Taylor series, cumulative distribution function (cdf), distribution function, root-finding methods