Timeline for Statistical test for boundedness of Expectation
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2018 at 19:31 | vote | accept | san | ||
| Apr 5, 2018 at 13:27 | comment | added | Iosif Pinelis | @michael : Please see the bottom of my answer. | |
| Apr 5, 2018 at 13:24 | comment | added | user83457 | There are techniques for estimating the tails of a distribution, which are appropriate for power laws, and depending on the power you get you believe your rv either has a mean or not. I remember one of them is called Hill's test, but I can't find it in Wikipedia. It and another technique are exposed in this book amazon.com/Quantitative-Risk-Management-Techniques-Princeton/dp/… | |
| Apr 5, 2018 at 13:13 | comment | added | Alejandro Nasif Salum | Cauchy distribution has no well defined expectation (and if we took the principal value of the corresponding integral, it would be finite)... Does this count as an 'unbounded mean'? I'm not sure what alternative hypothesis to finite expectation was assumed in the question... | |
| Apr 5, 2018 at 12:36 | comment | added | Iosif Pinelis | As the OP acknowledges in a comment to my answer, the question should have been expressed better. However, that same comment makes me think that there may indeed be research interest behind the question. | |
| Apr 5, 2018 at 1:43 | answer | added | usul | timeline score: 2 | |
| Apr 5, 2018 at 1:18 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
deleted 1 character in body
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| Apr 5, 2018 at 1:09 | answer | added | Iosif Pinelis | timeline score: 5 | |
| Apr 5, 2018 at 0:48 | answer | added | Bombyx mori | timeline score: 2 | |
| Apr 4, 2018 at 17:29 | comment | added | san | @MattF. I see, so with that method I need to be extremely lucky for it to work, way too many parametric families and that still will not cover all distributions. Any family that forms a net for distributions with infinite expectation ? | |
| Apr 4, 2018 at 17:21 | comment | added | user44143 | Of course, keep going with other families if you like, and keep testing to show that most do not provide good fits! This is just an example that would allow you to say: “the best fit among these two families of distributions has an undefined mean.” | |
| Apr 4, 2018 at 17:06 | history | edited | san | CC BY-SA 3.0 |
edited title
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| Apr 4, 2018 at 17:02 | review | Close votes | |||
| Apr 5, 2018 at 9:23 | |||||
| Apr 4, 2018 at 17:00 | comment | added | san | @MattF. But isn't Cauchy one of the infinitely many ways expectation can be unbounded, would testing for Cauchy test still be appropriate if the true distribution is different ? | |
| Apr 4, 2018 at 16:47 | comment | added | user44143 | Not in that form. But you can test: which fits this data better, a normal distribution or a Cauchy distribution? | |
| Apr 4, 2018 at 16:42 | review | First posts | |||
| Apr 4, 2018 at 16:44 | |||||
| Apr 4, 2018 at 16:37 | history | asked | san | CC BY-SA 3.0 |