AlphaSquared
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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[NormalDistributio n[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?
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[NormalDistributio
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?
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SOLUTION
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ASKER
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)