macro
zinvcdf p zp

#This macro accepts a specified p value and finds the corresponding zp value
#where p is the left tail area. The error is generally less than +/-0.001.

#Example calling statement:
#   mtb> %zinvcdf 0.025 k1
#Answer is z = -1.960.

#Copyright (c) Paul G. Mathews 9 Oct 01 All Rights Reserved
#Mathews and Malnar, Statistical Consultants and Trainers
#217 Third Street, Fairport Harbor, OH 44077
#440-350-0911   pmathews@apk.net

mcolumn pref zref pinterp zinterp
mconstant p zp n pgt50pct

#Here are the look-up tables for interpolation. Successive values of p are geometric
#progression with multiplicative factor of 1.25.

set pref
0.000100   0.000125   0.000156   0.000195   0.000244   0.000305&
0.000381   0.000477   0.000596   0.000745   0.000931   0.001164&
0.001455   0.001819   0.002274   0.002842   0.003553   0.004441&
0.005551   0.006939   0.008674   0.010842   0.013553   0.016941&
0.021176   0.026470   0.033087   0.041359   0.051699   0.064623&
0.080779   0.100974   0.126218   0.157772   0.197215   0.246519&
0.308149   0.385186   0.481482   0.500000   0.601853
end

set zref
3.71902   3.66226   3.60471   3.54634   3.48710   3.42697   3.36590&
3.30385   3.24077   3.17660   3.11130   3.04481   2.97705   2.90796&
2.83746   2.76546   2.69186   2.61657   2.53946   2.46041   2.37926&
2.29586   2.21000   2.12148   2.03005   1.93541   1.83724   1.73513&
1.62860   1.51708   1.39985   1.27602   1.14445   1.00366   0.85161&
0.68548   0.50110   0.29189   0.04643   0.00000  -0.25815
end

if p>0.5			#Does left tail calculation only so fix p if necessary
   let pgt50pct=1
   let p=1-p
else
   let pgt50pct=0
endif

let n=2			#Start through the look-up table
while p>pref(n)
   let n=n+1
endwhile

let pinterp(1)=pref(n-1)	#Map the three values for quadratic interpolation
let pinterp(2)=pref(n)
let pinterp(3)=pref(n+1)
let zinterp(1)=zref(n-1)
let zinterp(2)=zref(n)
let zinterp(3)=zref(n+1)

%quadinterp pinterp zinterp p zp	#Call the quadratic interpolation macro
let zp=-round(zp,3)	
if pgt50pct
   let p=p+0.5
   let zp=-zp
endif

print p zp
#invcdf p				#For checking the answer if required

endmacro