Inverse cumulative normal distribution

01122016, 10:16 PM
(This post was last modified: 01132016 06:41 AM by Pekis.)
Post: #1




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^31.5976*x}) I simply inverted the function to let Wolfram solve a*y^{3}+b*yln(1/x1)=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/x1)+sqrt(ln^{2}(1/x1)+4b^{3}/(27a^{2})) then Phi^{1}(x)=(t(x)/(2a))^{1/3}(2b^{3}/(27a^{2}t(x)))^{1/3} It seems OK with 3 decimals on all range ]01[ ... What do you think ? 

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Messages In This Thread 
Inverse cumulative normal distribution  Pekis  01122016 10:16 PM
RE: Inverse cumulative normal distribution  Pekis  01132016, 08:45 AM
RE: Inverse cumulative normal distribution  Pekis  01132016, 09:54 AM
RE: Inverse cumulative normal distribution  Dieter  01132016, 01:28 PM
RE: Inverse cumulative normal distribution  Dieter  01132016, 11:09 PM

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