Timeline for Monotone likelihood ratio of convolved power function kernel, $p\ge 3$
Current License: CC BY-SA 4.0
34 events
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| S Sep 8, 2023 at 1:00 | history | bounty ended | CommunityBot | ||
| S Sep 8, 2023 at 1:00 | history | notice removed | CommunityBot | ||
| Sep 7, 2023 at 7:19 | comment | added | japalmer | Is there an integral representation of $f(x)$ that satisfies the differential inequality? | |
| Sep 2, 2023 at 9:57 | comment | added | David Roberts♦ | 25 edits in a week. As I said last time, excessive editing is frowned on here, and the software flags posts with many self-edits. Please avoid this in future. | |
| Sep 2, 2023 at 2:00 | history | edited | japalmer | CC BY-SA 4.0 |
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| Sep 2, 2023 at 1:51 | history | edited | japalmer | CC BY-SA 4.0 |
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| Sep 2, 2023 at 1:41 | history | edited | japalmer | CC BY-SA 4.0 |
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| Sep 1, 2023 at 21:51 | history | edited | japalmer | CC BY-SA 4.0 |
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| Sep 1, 2023 at 21:36 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 31, 2023 at 1:42 | history | edited | japalmer | CC BY-SA 4.0 |
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| S Aug 30, 2023 at 23:40 | history | bounty started | japalmer | ||
| S Aug 30, 2023 at 23:40 | history | notice added | japalmer | Draw attention | |
| Aug 28, 2023 at 1:53 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 27, 2023 at 16:32 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 27, 2023 at 16:06 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 27, 2023 at 14:52 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 26, 2023 at 16:21 | history | edited | japalmer | CC BY-SA 4.0 |
Modified after realizing the result doesn't hole for $2 < p < 3$.
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| Aug 26, 2023 at 15:49 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 26, 2023 at 6:24 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 26, 2023 at 2:52 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 26, 2023 at 1:54 | history | edited | japalmer | CC BY-SA 4.0 |
Should be last formatting edit
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| Aug 26, 2023 at 1:39 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 25, 2023 at 23:21 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 25, 2023 at 18:50 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 25, 2023 at 18:31 | comment | added | Michael Hardy | The integral$$ \int_0^{\pi/2} \Big(f\big(\hspace{-1pt}\cos(\varphi-\theta)\big) - f\big( \hspace{-1pt}\cos(\varphi+\theta)\big) \Big) \frac{\sin(2\varphi)}{\sin(2\theta)} \, d\varphi$$ does not depend on the value of $\theta\in(0,\pi/2).$ If that's what you had in mind, could you state that explicitly at the beginning of the question? | |
| Aug 25, 2023 at 16:10 | comment | added | japalmer | I meant that it can be shown that the integral over $\phi$ is independent of $\theta$, so it's a density except for a normalizing term (e.g. see "answer link in first sentence). | |
| Aug 25, 2023 at 16:03 | comment | added | Michael Hardy | $$ \begin{align} p(\varphi;\theta) = {} & \Big(f\big(\hspace{-1pt}\cos(\varphi-\theta)\big) - f\big( \hspace{-1pt}\cos(\varphi+\theta)\big) \Big)\hspace{0.5pt} \frac{\sin(2\varphi)}{\sin(2\theta)}, \\ & \text{for } 0 < \varphi,\theta < \frac{\pi}{2} \end{align} $$ You call this a "density". Did you mean that as a function of $\varphi$ with $\theta$ fixed, it is a probability density? | |
| Aug 25, 2023 at 14:19 | history | asked | japalmer | CC BY-SA 4.0 |