Timeline for Normal multivariate orthant probabilities
Current License: CC BY-SA 4.0
15 events
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| Jun 5, 2022 at 15:14 | comment | added | RobHarley |
asin3( a, b, c ) = intnum( th = 0, asin( b ), asin( a * sin( th ) * c / sqrt( cos( th )^2 - a^2 ) / sqrt( cos( th )^2 - c^2 ) ) );
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| Jun 5, 2022 at 14:38 | comment | added | RobHarley | Or use the change of variables beta = sin( theta ) for improved accuracy in edge cases. | |
| Jun 5, 2022 at 14:37 | comment | added | RobHarley |
asin3( a, b, c ) = intnum( be = 0, b, asin( a * be * c / sqrt( 1 - a^2 - be^2 ) / sqrt( 1 - be^2 - c^2 ) ) / sqrt( 1 - be^2 ) );
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| Jun 4, 2022 at 12:55 | comment | added | user44143 | @TMM, you are right. I will leave my comment up in case anyone else thinks the answer looks simple. | |
| Jun 4, 2022 at 12:35 | comment | added | TMM | @MattF. No, it's not. The single-argument arcsin is a 1D integral, the 3-argument arcsin is a 1D integral over the single-argument one, and the 5-argument arcsin is a 1D integral over the 3-argument one. So it's a large number of 3D integrals which all need to be computed, which is probably still very hard to do accurately. | |
| Jun 3, 2022 at 1:45 | comment | added | user44143 | @TMM, this is a conversion from a six-dimensional integral to one-dimensional integrals, so I think it does count as a simplification — indeed this answer would be easy to evaluate numerically while the original integral would not be. | |
| May 4, 2022 at 2:23 | comment | added | TMM | And for what it's worth, the extra digits (assuming they are accurate) suggest there is no nice expression hidden there: wayback.cecm.sfu.ca/cgi-bin/isc/… | |
| May 4, 2022 at 2:22 | comment | added | TMM | Thanks for the answer, but I'm not sure this simplifies anything - the original question involved an integral, and the answer now contains dozens of integrals that need to be evaluated. Maybe it helps with numerical evaluation of the result though. | |
| May 3, 2022 at 16:43 | history | edited | RobHarley | CC BY-SA 4.0 |
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| May 3, 2022 at 14:17 | history | edited | RobHarley | CC BY-SA 4.0 |
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| May 3, 2022 at 7:37 | comment | added | Alex M. | While this answer one of the questions asked by the OP, it clearly is not enlightening. These computations look as if they were performed by a computer algebra system (which one?), so why not add the commands (program) that you used to produce them? | |
| May 3, 2022 at 1:36 | history | edited | RobHarley | CC BY-SA 4.0 |
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| May 3, 2022 at 1:32 | review | Late answers | |||
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| S May 3, 2022 at 1:15 | review | First answers | |||
| May 3, 2022 at 7:37 | |||||
| S May 3, 2022 at 1:15 | history | answered | RobHarley | CC BY-SA 4.0 |