macro
normal z cdf

#This macro finds the area under the left tail of the normal distribution
#relative to the specified z value. The answer is a constant called cdf.

#z is the standard normal z value
#cdf is the area under the normal curve in the left tail relative to z

#Example calling statement:
#   mtb> %normal 2.0 k1
#Answer cdf = 0.977252

#Algorithm from AMS55 p. 932 26.2.10 for z>0
#Copyright (c) Paul G. Mathews 8 Oct 01 All Rights Reserved

mconstant z cdf term err n lastcdf negative

let negative=(z<0)
let z=abs(z)
let term=z			#first term in the summation
let cdf=z
let err=1
let n=1
while err>1e-4
   let lastcdf=cdf
   let term=term*(-1)*z*z/n/2
   let cdf=cdf+term/(2*n+1)
   let err=abs(1-lastcdf/cdf)
   let n=n+1
endwhile
let cdf=0.5+cdf/sqrt(2*3.14159)
if negative
   let cdf=1-cdf
endif

print z cdf
endmacro