NormProb ( x )

Returns the Gaussian Probability Integral

Average rating: 4.2 (37 votes) Log in to vote

Dr. Ronald W. Satz - Show more from this author
Transpower Corporation
http://www.transpowercorp.com

Sample input:

NormProb ( 2 )

Sample output:

.977249867045

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

/* Returns the Gaussian (Normal) probability integral to the left of x--the left-tail probability.  For right-tail probabilities, call with
argument -x.  Algorithm is #209 from the ACM, by D. Ibbetson.  Also used in TrueBasic Stat1 Library.   Should be accurate to 8 decimal places. */

Let ( [  ya = (Abs(x)) /2 ;
            w = ya^2 ;
            za = ((    .000124818987)*w - .001075204047)*w ;
            zb = ((za + .005198775019)*w - .019198292004)*w ;
            zc = ((zb + .059054035642)*w - .151968751364)*w ;
            zd = ((zc + .319152932694)*w - .5319230073)*w ;
            ze =  (zd + .797884560593)*ya*2 ;
            yb = ya-2 ;
            zf = -.000045255659*yb ;
            zg = ((zf + .00015252929)*yb - .000019538132)*yb ;
            zh = ((zg - .000676904986)*yb + .001390604284)*yb ;
            zi = ((zh - .00079462082)*yb - .002034254874)*yb ;
            zj = ((zi + .006549791214)*yb - .010557625006)*yb ;
            zk = ((zj + .01163044731)*yb - .009279453341)*yb ;
            zl = ((zk + .005353579108)*yb - .002141268741)*yb ;
            zm = ((zl + .000535310849)*yb + .999936657524) ] ; 

Case
          (
            x = 0 ; .5  ; /* special case for origin */
            ya ≥ 3 and x > 0 ; 1 ; 
            ya  ≥ 3 and x <  0 ; 0 ;  /* way out in the tails */
            ya < 1  and x > 0 ; (1 + ze) / 2 ;
            ya < 1 and x < 0 ; (1 - ze ) / 2 ;
            x > 0 ; (1 + zm) / 2 ;
            x < 0  ; (1 - zm) / 2 ;
            " "
           )
         )

This custom function returns the Gaussian (Normal) probability integral (area under the Bell curve) to the left of x (including the area to the left of the y axis). This is the left-tail of the probability distribution. To get the right-tail (which is 1 - NormProb (x)), call the function with the argument -x.

Comments

Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

NormProb ( x )

Comments

Support this website.

Support this website.