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GAMMA PARAMETER OUTPUT: NLGGAM .. NATURAL LOGARITHM OF GAMMA(ALPHA) LOCAL: ... 62. 3 1 1. 7 These results agree with those published in tables (Pearson, 1965). Notes 1. The result will be accurate to at least 9 decimal digits given that the computer is capable of such accuracy. 2. High values of ALPHA have the potential to cause overflow. The program is interrupted if ALPHA is greater than lE7. This limiting value may be adjusted to suit the capacity of the reader's machine. 34 Advanced BASIC Scientific Subroutines RATIO OF THE INCOMPLETE GAMMA FUNCTION Subroutine: GAMMFN Description Evaluates the ratio of the incomplete gamma function G (p, y) to the complete function r(p) for p > 0, y > 0.

Where L is the mean of the distribution. In the subroutine use is made of the relationships: Px(X= t) =(L/t)px(X= t - 1) t = 1,2 ... The distribution function F x(t), the probability of t or fewer events, is given by t Fx(t)= ~ Px(X=k) t=O, 1,2 ... k=O The probability of t or more events is P(X~t) = 1- =1 t-l ~ k=O P(X=k) t= 1,2 ... t = ° Subroutine Listing 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 2130 REM REM REM REM REM REM REM REM REM REM REM REM REM REM POISSON PROBABILITY AND DISTRIBUTION FUNCTION SUBROUTINE: POISPD EVALUATES P(X = T), P(X (= T) AND P(X FOR A POISSON DISTRIBUTION >= T) VARIABLES: INPUT: L1 ......

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.