Timeline for Estimate of a ratio of two incomplete gamma functions
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2014 at 22:23 | vote | accept | pwl | ||
| Aug 22, 2014 at 17:34 | answer | added | Sergei | timeline score: 2 | |
| Oct 1, 2013 at 12:04 | vote | accept | pwl | ||
| Aug 22, 2014 at 22:23 | |||||
| Sep 30, 2013 at 13:00 | history | edited | pwl | CC BY-SA 3.0 |
Fixed the dependence on the sign of $(\alpha-\beta)$
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| Sep 30, 2013 at 12:58 | answer | added | pwl | timeline score: 2 | |
| Sep 30, 2013 at 12:45 | comment | added | pwl | @suvrit How exactly do you plan to minimize the denominator? By taking $x\to y$ or vice versa? Anyway, this would result in denominator equal to zero. I tried maximizing/minimizing the term $e^{-t}$ which for numerator is $e^{-y}$ and for denominator is $e^{-x}$ but this gives an estimate $\dots<e^{x-y}\frac{\beta}{\alpha}\frac{x^\alpha-y^\alpha}{x^\beta-y^\beta}$ which is far from optimal due to $e^{x-y}$ term. | |
| Sep 29, 2013 at 17:19 | comment | added | Suvrit | By writing the first ratio as a ratio of integrals, what do you get if you maximize the numerator and minimize the denominator? That should yield a trivial upper bound? Is it easy to do this for $\frac{\int_y^x t^{\alpha-1}e^{-t}}{\int_y^x t^{\beta-1}e^{-t}}$? | |
| Sep 29, 2013 at 15:04 | history | edited | Ricardo Andrade |
added top level tag
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| Sep 29, 2013 at 9:32 | history | asked | pwl | CC BY-SA 3.0 |