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Hi,
I was looking for an algorithm that will tell me the z-score of a
given percentile. In other words, I was looking for an algorithm
that will replicate a reverse lookup in a normal distribution table.
Abramowitz & Stegun is my friend ("Handbook of Mathematical
Functions"). Formula 26.2.22 gives an approximation in z accurate to
within 3e-3, and formula 26.2.23 gives a more complicated but more
accurate formula.
26.2.22 says this (in pseudo-Fortran). p appears to be the
*upper*-tail probability (ie. p=P(Z>z)) and has to be less than 0.5
for this to work. (If not, call the function with argument 1-p and
put
a minus sign on the result.)
t=sqrt(ln(1/p**2)) [ p squared ]
a0=2.30753
a1=0.27061
b1=0.99229
b2=0.04481
z=t-(a0+a1*t)/(1-t*(b1+b2*t))
The problem is to implement this effeciently in AB. Ay ideas?
Thanks,
Pal
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