Timeline for When does positive skew imply median<mean?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Apr 4 at 14:58 | comment | added | jbowman | @MattF. - yep! And I upvoted it too! | |
| Apr 4 at 12:36 | comment | added | user225256 | @jbowman, now that you can see the first part of the OP’s answer…that seems meaningful to me! | |
| Apr 4 at 0:42 | answer | added | Simon Segert | timeline score: 1 | |
| Apr 3 at 15:14 | history | made wiki | Post Made Community Wiki by whuber♦ | ||
| Apr 3 at 15:02 | comment | added | jbowman | I don't see why you think @whuber's characterization is either unfair or dismissive. He's basically saying that he doesn't believe there's going to be a meaningful answer—one other than what you've already classified as "trivial," and he outlines his reasons why. He's not the only one—I doubt it, too, and statsplease below apparently does as well. | |
| Apr 3 at 14:49 | answer | added | user225256 | timeline score: 1 | |
| Apr 3 at 14:45 | history | edited | Simon Segert | CC BY-SA 4.0 |
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| Apr 3 at 14:28 | comment | added | Simon Segert | @whuber I really find this characterization quite unfair and dismissive. Insofar as modern probability theory is based on the language of mathematics which is itself based on the language of set theory, basically any question one could possibly ask would ultimately come down to "describing some region (set)". Clearly some descriptions are more nice or probabilistically meaningful than others- the criteria for what makes a description nice are admittedly sociological, but I don't think that makes the question ill-posed. | |
| Apr 3 at 14:09 | comment | added | whuber♦ | @Matt Geometrically, this question is the same as (say) describing a region $R$ in the plane with a simple formula and asking for other formulas that would describe that region, too. The "plane" is really the space of all distributions with a natural topology (such as convergence in distribution). Literally any answer will be of the form "well, if you restrict to such-and-such a subset of the plane [that is, a specified family of distributions], then here's a different-looking characterization of its intersection with $R$." I find that too broad and vague to be suitable here. | |
| Apr 3 at 14:06 | comment | added | user225256 | @whuber, why such pessimism? Eg: A nice condition for mean>median in the exponential family of distributions would seem both plausible and of interest. | |
| Apr 2 at 13:36 | history | edited | Simon Segert | CC BY-SA 4.0 |
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| Apr 1 at 19:38 | comment | added | whuber♦ | My point is that it's unlikely you will find anything other than a direct restatement of the original condition. | |
| Apr 1 at 19:21 | comment | added | Simon Segert | @whuber, I'm not sure I understand your objection. Ultimately there's some set S of distributions with the desired property, and I'm asking for a sufficient condition on $X$ that ensures $X\in S$. The fact that you can perturb a distribution in S to bump it out of S or vice versa doesn't imply that there can't be an interesting answer to that question (besides I'm not sure I would consider the changes you describe as "arbitrarily tiny", but that is beside the point). | |
| Apr 1 at 18:33 | comment | added | whuber♦ | The comment by @stats has considerable force. No answer will be satisfactory, because you can change $X$ in arbitrarily tiny ways while effecting arbitrarily large and different changes in the skewness and mean. (Merely contaminate $X$ with a suitable atomic distribution.) Thus, trivial results can be asserted: e.g., people can reference families of distributions where this equivalent always holds, but that's of little or no interest because it's just a property of the family and not of random variables generally. | |
| Apr 1 at 12:50 | comment | added | kjetil b halvorsen♦ | Some similar Qs Why is the arithmetic mean > median on a histogram skewed to the right?, Empirical relationship between mean, median and mode, | |
| Apr 1 at 10:43 | history | became hot network question | |||
| Apr 1 at 10:21 | answer | added | statsplease | timeline score: 4 | |
| Apr 1 at 2:49 | history | edited | Simon Segert | CC BY-SA 4.0 |
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| Apr 1 at 2:24 | history | asked | Simon Segert | CC BY-SA 4.0 |