By B.V. Cordingley, D.J. Chamund
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The ratio between terms is determined with the aid of rea + 1) = area) and is used to facilitate summation. The process is terminated when the required accuracy is achieved. If p < (p + q)x then Ix -1 (q, p) is found by the above method and the equation Ix(p,q) = l-Ix_1 (q,p) used to determine Ix(P, q). Ln B(p, q) is evaluated with the help of subroutine LNGAMM which determines In r (a) for a > 1. DT BETWEEN T = 0 AND T = X, WHERE P>=O, Q>=O, O<=X<=l. ALSO COMPUTES LN(B(P,Q». REQUIRES SUBROUTINE LNGAMM VARIABLES: INPUT: NLGGAM ..
F. 98 2E-2 44 Advanced BASIC Scientific Subroutines These results agree with those published in statistical tables for x: . Note See the section on GAMMFN for comments on precision and magnitude of m andx. The Subroutines 45 UPPER TAIL AREA OF THE F-DISTRIBUTION Subroutine: FDISTR Description Computes the area under the upper tail of the F-distribution for (m, n) degrees of freedom. Requires subroutines BETAFN and LNGAMM. Method The integral of the upper area of the F-distribution, 1 - F(z), is solved with the aid of the subroutine for the incomplete beta function BETAFN.
L1 PRINT II DENSITY = ". DFX PRINT" AREA UNDER CURVE ". FX >RUN TIME = 50. 006312. 31 The Subroutines NATURAL LOGARITHM OF THE COMPLETE GAMMA FUNCTION Subroutine: LlVGAAfAf Description Evaluates the natural logarithm of the complete gamma function rea) for a > O. 5ln(27T) + ~ n=l :n_ (l)n-l B - 2n(2n - 1)x n 1 where B 2n are the Bernoulli numbers. Subroutine Listing 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 2130 2140 2150 2160 2170 REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM NATURAL LOGARITHM OF GAMMA FUNCTION SUBROUTINE: LNGAMM EVALUATES THE NATURAL LOGARITHM OF THE GAMMA FUNCTION FOR PARAMETER ALPHA FOR ALPHA> O.