Link to home
Start Free TrialLog in
Avatar of AlphaSquared
AlphaSquared

asked on

Given a percentile input, calculate the number of standard deviations from 0 using a normal distribution

I need to reverse engineer an old function.  Before I came into the picture my friend had a hard drive crash and lost the original documentation and source code, no backups, OH MY!  :

We only have a short description left:

Function: NormalCDF(Percentile), returns the number of standard deviations "Percentile" is from 0
using the standard normal distribution with mean 0 and standard deviation 1.

The name of the function seems misleading to me, At first I thought it referred to the cumulative distribution function (CDF) of a normal distribution.  But that doesn't seem to make sense from the description.

I'll use Mathematica to implement the new version of this.  It has an internal function to generate a Normal distribution with mean 0 and standard deviation 1:

    NormalDistribution[0, 1]

Maybe the cumulative distribution function has some equivalence to "the number of standard deviations "Percentile" is from 0..."

I can also plot a CDF of the normal distribution like this:

Plot[CDF[NormalDistribution[0, 1], x], {x, -4, 4}]

but I don't feel like this gets me on the right track.

Regardless of the name of the function I need to do this:

Given a percentile input, calculate the number of standard deviations from 0 using a normal distribution

Any ideas?
ASKER CERTIFIED SOLUTION
Avatar of ozo
ozo
Flag of United States of America image

Link to home
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
Start Free Trial
SOLUTION
Link to home
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
Start Free Trial
Avatar of AlphaSquared
AlphaSquared

ASKER

Figured it out. thanks to both of you for moving my thoughts along.

The inverse of the cumulative normal distribution does the trick

Then      
     z=Q^{-1}(x/100)
where x = percentile (x = 75) then the z score corresponding to the 75 percentile =:
     z=Q^{-1}(0.75)