IS there a mathematical formula for NORMSINV?

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

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

"SyBorg" wrote:

> 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