By B.V. Cordingley, D.J. Chamund
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Extra info for Advanced BASIC Scientific Subroutines
2 Probability, Density and Distribution Functions BINOMIAL PROBABILITY AND DISTRIBUTION FUNCTION Subroutine: BINOPD Description Evaluates the probability of both obtaining a specified number of successes and of obtaining from zero to the specified number of successes in a binomial trial. Method If X is a binomial random variable then Px(X=t)= (~)ptqn-t t=O, 1,2 ... n = 0 otherwise where n is the number of trials, p the probability of a success on a single trial and q = 1 -po In the subroutine use is made of the relationships: Px(X= t)=qn t =0 Px(X= t)= ((n + 1- t)/t) (P/q)px(X= t - 1) Fx(t) =Px(X~ t) t =~ Px(k) t t = 1,2 ...
DF1 4370 PRINT" DF2 = "; DF2; ". XF = "; XF 4380 END "; DF1 Sample Program Use the F-distribution to determine the probability of obtaining values for the F-ratio, s~, greater than those shown in the table. m and n are the number of degrees of freedom corresponding to s1 and s~ respectively. 8 8 4 SAMPLE PROGRAM: PFDISTR COMPUTES THE UPPER-TAIL AREA OF THE F-DISTRIBUTION FOR N1 SETS OF DATA DATA 1. 1. 86. 5. 3. 31. 4. 30. 69 DATA 24. 6. 84. 24. 30. 47. 8. 1. 5982 DATA 8. 4. 0. 8. 4. 8 PRINT HEADINGS.
Ifp ~ (p + q)x, the resulting series I (p q) = x , r(p + q)xP(1 - X)q-1 + I (p + 1 q _ rep + 1) rep) x , 1) (2) is evaluated up to s times where s = INT(q + (1 -x) (p + q» (3) The process is continued if necessary with the aid of the recurrence relation: Ix(p+s,q-s)=: rep + q)xP+S(1 x)q-s +Ix(p+s+l,q-s) r(p + s + 1) r(q - s) (4) If (3) does not produce a positive integer then only equation (4) is employed. The ratio between terms is determined with the aid of rea + 1) = area) and is used to facilitate summation.