Timeline for Probability distribution function expressed in terms of a divergent series
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
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| Jan 22, 2020 at 5:26 | history | edited | William | CC BY-SA 4.0 |
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| S Jan 21, 2020 at 22:19 | history | bounty ended | William | ||
| S Jan 21, 2020 at 22:19 | history | notice removed | William | ||
| Jan 21, 2020 at 3:01 | history | tweeted | twitter.com/StackStats/status/1219454964986208259 | ||
| Jan 21, 2020 at 2:49 | vote | accept | William | ||
| Jan 21, 2020 at 1:36 | vote | accept | William | ||
| Jan 21, 2020 at 1:36 | |||||
| Jan 21, 2020 at 0:23 | answer | added | whuber♦ | timeline score: 6 | |
| Jan 20, 2020 at 20:03 | history | edited | William |
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| S Jan 20, 2020 at 8:32 | history | bounty started | William | ||
| S Jan 20, 2020 at 8:32 | history | notice added | William | Authoritative reference needed | |
| Jan 20, 2020 at 5:18 | history | edited | William | CC BY-SA 4.0 |
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| Jan 19, 2020 at 0:06 | comment | added | William | Let us continue this discussion in chat. | |
| Jan 18, 2020 at 21:02 | comment | added | William | @whuber I've corrected it, I've added $\theta^n$ in the denominator. Any way, still wondering if any answer to my previous comment. | |
| Jan 18, 2020 at 21:00 | history | edited | William | CC BY-SA 4.0 |
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| Jan 18, 2020 at 20:48 | comment | added | William | @whuber are you saying that when $\alpha =1, k=1, R=1$ the series converges to $(y^2+2e^{-y}(y+1)-2)/y^2$? If yes, how did you get that? | |
| Jan 18, 2020 at 20:38 | comment | added | whuber♦ | It must have been. There are some simple checks. One of them is that because $\theta$ is a scale parameter for $g,$ it must be a scale parameter for $U_i,$ whence the CDF must be a function of $y/\theta$--but it is not. Another is to plug in simple values of parameters. E.g., $\alpha=1,$ $k=1,$ $R=1$ gives a sum that evaluates to $(y^2 + 2e^{-y}(y+1)-2)/y^2,$ which works, so you might be close. | |
| Jan 18, 2020 at 20:29 | comment | added | William | If it's not a CDF then was my derivation wrong? | |
| Jan 18, 2020 at 20:18 | comment | added | whuber♦ | That's irrelevant, because a more basic problem is that $F_{U_i}$ obviously is not a CDF, since it is directly proportional to $\theta^{-k}.$ Thus, there is at most one $\theta$ that could possibly make this a valid CDF and for arbitrary $\theta$ and $k$ it cannot be a CDF. | |
| Jan 18, 2020 at 20:04 | comment | added | William | @whuber if it converges how do you proof $\int_0^\infty f_{U_i}(y) dy=1$? | |
| Jan 18, 2020 at 15:12 | comment | added | whuber♦ | Please explain why you think this series diverges. As far as I can tell, for most values of $\alpha$ (including all positive values) it is an entire function: it converges everywhere in the complex plane. | |
| Jan 18, 2020 at 6:39 | history | asked | William | CC BY-SA 4.0 |