Timeline for Approximation of a normal distribution function
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 9, 2017 at 17:36 | comment | added | Yoav Kallus | The down voter was I (now reversed). Thanks for the explanation, which explains what your approximation is trying to optimize. Note that the OP asked about approximation for $x>8.2$, for which your approximation, while OK in terms of absolute difference between the actual value and the approximation, is bad in terms of relative difference. | |
| Aug 9, 2017 at 16:52 | comment | added | Alt | I needed a fast way of computing the normal CDF, and the similarity in the shape of this function and the sigmoid function ($\sigma(t) = \frac{1}{1+e^{-t}}$) attracted my attentions. Then, I ran a computer simulation to tune the coefficient $a$ such that $\int_{x1}^{x2}\|\Phi(x)-\sigma(at) \|_2^2dx$ is minimized for some large magnitude negative $x_1$ and positive $x_2$. $a$ turned out to be $−1.65451$. | |
| Aug 9, 2017 at 16:19 | comment | added | Igor Rivin | It certainly is not mine, but I am guessing the downvoter was frustrated to not know where this expression came from. | |
| Aug 9, 2017 at 16:02 | history | edited | Alt | CC BY-SA 3.0 |
deleted 33 characters in body
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| Aug 4, 2017 at 1:50 | comment | added | Alt | What is the downvote for? | |
| Jul 5, 2017 at 19:59 | review | Low quality posts | |||
| Jul 5, 2017 at 21:36 | |||||
| Jul 5, 2017 at 17:03 | history | answered | Alt | CC BY-SA 3.0 |