Timeline for Does mean=mode imply a symmetric distribution?
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| Oct 17, 2019 at 23:00 | comment | added | Glen_b | However, if we choose another measure of skewness as our standard (say mean-median skewness) then we can certainly have that and third-moment skewness being of opposite sign. | |
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Oct 6, 2016 at 13:54 | comment | added | Glen_b | @Christoph That is indeed the difficulty -- outside a specified measure of skewness, how are we to decide if a distribution is skewed to the left? (In some cases, it's obvious enough, but in many cases it isn't. | |
| Oct 6, 2016 at 13:45 | comment | added | Christoph Hanck | @Glen_b: Would it be a duplicate to ask a separate question about the signs of the skewness coefficient $sk=E(X-\mu)^3$? E.g., if $sk>0$, does that imply that the distribution is skewed to the left - assuming a proper definition for such a situation exists in the first place? | |
| Oct 2, 2016 at 23:51 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Oct 2, 2016 at 1:43 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Oct 2, 2016 at 0:48 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Oct 2, 2016 at 0:44 | comment | added | Glen_b | @NickT No, you can have mean=median=mode and every odd moment 0 but still have asymmetry. I was considering putting that in as well, after I added the bit about the third moment.. Looks like I should have. I have linked to some other posts that deal with the "all odd moments" part and discuss why you can still get mean=median=mode as well. | |
| Oct 1, 2016 at 17:00 | comment | added | Nick T | If all the (odd?) moments beyond the variance are 0, would that only happen iff there's a symmetric distribution? | |
| Oct 1, 2016 at 7:39 | vote | accept | tzipy | ||
| Oct 1, 2016 at 6:14 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Oct 1, 2016 at 1:44 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 30, 2016 at 7:22 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 30, 2016 at 6:24 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 30, 2016 at 4:25 | comment | added | Glen_b | @HongOoi I have added another example. | |
| Sep 30, 2016 at 4:25 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 30, 2016 at 2:21 | comment | added | Glen_b | @HongOoi I expect you mean to ask how far you can get rather than how close (since obviously you can make it perfectly symmetric any time you want). You can make it a good deal more asymmetric than my example -- it was just a convenient case. | |
| Sep 30, 2016 at 2:06 | comment | added | Hong Ooi | An interesting question might be how "close" to symmetry can you get with these properties. Looking at your discrete example, it's kind-of sort-of symmetric with a hump in the middle. | |
| Sep 30, 2016 at 1:45 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 30, 2016 at 1:35 | comment | added | Kodiologist | I think the moral of the story is: symmetry is a strong property and can't be deduced from a few typical summary values of the distribution. | |
| Sep 30, 2016 at 1:33 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 30, 2016 at 0:15 | history | answered | Glen_b | CC BY-SA 3.0 |