Timeline for Pade approximation of gaussian distribution to given precision
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2019 at 6:10 | comment | added | Federico Poloni | Consider asking on Computational Science: there are more experts there on actually computing stuff numerically, and I wouldn't be surprised if someone has already encountered this exact same problem. | |
| Sep 19, 2019 at 4:04 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Jul 22, 2016 at 5:48 | comment | added | Michael | @MattF.: Does indefinite integral has the closed form? I won't integrate to $\infty$. | |
| Jul 22, 2016 at 5:46 | comment | added | Michael | @BrianBorchers: Things like that, but possibly with different values of $c$ in the kernel of $e^{-x^c-y^c}$. The case $c=2$, a.k.a. Gaussian distribution, is the one that led to the question and is the most useful for this application. However, the case $c=1.5$, a.k.a. Holtsmark distribution, is also very useful in that context. | |
| Jul 22, 2016 at 4:23 | comment | added | user44143 | If all you need is the definite integral $\int_{-\infty}^{\infty} \exp(-x^2)\,\text{erf}(x+a)\,dx$, it has the closed form $\sqrt{\pi}\, \text{erf}(a/\sqrt{2})$. Mathematica does not know this, but it is 4.3.13 in Geller and Ng's paper at nvlpubs.nist.gov/nistpubs/jres/73B/jresv73Bn1p1_A1b.pdf. You can prove it by expanding erf as an integral of $y$, and then changing variables with a 45-degree rotation of the $xy$-plane. | |
| Jul 22, 2016 at 4:08 | answer | added | Manfred Weis | timeline score: 0 | |
| Jul 22, 2016 at 0:48 | comment | added | Brian Borchers | You'd do well to explain exactly what integral you actually want to evaluate. It seems unlikely that the strategy you're suggesting would be optimal. Is it just $\int_{-\infty}^{c} e^{-x^2 }\mbox{erf}(x+a)dx$? | |
| Jul 22, 2016 at 0:30 | comment | added | Michael | @BrianBorchers: edited the question with the reason why I need that. | |
| Jul 22, 2016 at 0:30 | history | edited | Michael | CC BY-SA 3.0 |
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| Jul 22, 2016 at 0:13 | comment | added | Brian Borchers | Do you need to compute the Gaussian probability density or the comulative desnity (integral of the pdf from $-\infty$ to $x$) The former is trivial using an $\exp$ library function. The second is actually somewhat of a challenge. | |
| Jul 21, 2016 at 23:10 | answer | added | J.J. Green | timeline score: 3 | |
| Jul 21, 2016 at 22:12 | history | asked | Michael | CC BY-SA 3.0 |