IS there a mathematical formula for NORMSINV?

[SyBorg]

I'm trying to verify the calculation for the Inverse Cumulative Standard
Normal Distribution Function (also known as the Probit function) represented
by the Excel function NORMSINV( ).

For instance: The Excel function =NORMSINV(0.9626) returns 1.78.

Can someone show me a manual calculation for this? I'm currently digging
through the statistics books, but hoping for a quick-n-dirty solution.

Thanks,

- George

 

[Jerry W. Lewis]

To check the calculation,
=ABS(NORMSDIST(NORMSINV(p))-p)
should be be small (relative to p).

NORMSDIST is and integral that has no simple closed form. Some
approximations are given in
http://www.math.sfu.ca/~cbm/aands/page_932.htm
http://www.math.sfu.ca/~cbm/aands/page_933.htm

NORMSDIST(x) and NORMSINV(p) are reasonably accurate (~4-6 figures) in all
versions for ABS(x)<4 which correspons to MIN(p,1-p)>3E-5. If you need to go
farther into the tails, then you either need Excel 2003, or Ian Smith's
library of probability functions
http://members.aol.com/iandjmsmith/Examples.xls

Jerry