Inverse cumulative normal distribution
01-12-2016, 10:16 PM (This post was last modified: 01-13-2016 06:41 AM by Pekis.)
Post: #1
 Pekis Member Posts: 103 Joined: Aug 2014
Inverse cumulative normal distribution
Hello,

Here is what seems a good rough approximation of the inverse cumulative normal distribution (Phi-1(x)) :

Originally based on A logistic approximation to the cumulative normal distribution

It claims a maximum error less than 1.4*10-4 on all range with this function
Phi(x)=1/(1+e-0.07056x^3-1.5976*x)

I simply inverted the function to let Wolfram solve a*y3+b*y-ln(1/x-1)=0 on y (where a=-.07056 and b=-1.5976)

I got a somehow gory formula which can be a bit simplified:
If a=-0.07056 and b=-1.5976 and t(x)=ln(1/x-1)+sqrt(ln2(1/x-1)+4b3/(27a2))
then Phi-1(x)=(t(x)/(2a))1/3-(2b3/(27a2t(x)))1/3

It seems OK with 3 decimals on all range ]0-1[ ... What do you think ?
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 Messages In This Thread Inverse cumulative normal distribution - Pekis - 01-12-2016 10:16 PM [] - Dieter - 01-12-2016, 11:38 PM RE: Inverse cumulative normal distribution - Pekis - 01-13-2016, 08:45 AM RE: Inverse cumulative normal distribution - Pekis - 01-13-2016, 09:54 AM RE: Inverse cumulative normal distribution - Dieter - 01-13-2016, 01:28 PM RE: Inverse cumulative normal distribution - Dieter - 01-13-2016, 11:09 PM

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