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Dec 8, 2017 at 14:10 comment added Iosif Pinelis I have added a remark (highlighted) explaining why one should choose a finite negative $q$ to measure the distances from potential outliers to the rest of the data.
Dec 8, 2017 at 14:07 history edited Iosif Pinelis CC BY-SA 3.0
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Dec 8, 2017 at 3:31 history edited Iosif Pinelis CC BY-SA 3.0
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Dec 8, 2017 at 3:11 history edited Iosif Pinelis CC BY-SA 3.0
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Dec 8, 2017 at 3:02 history edited Iosif Pinelis CC BY-SA 3.0
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Dec 7, 2017 at 23:16 comment added Iosif Pinelis Good point! Yes, this looks really unbelievable, until one looks at it a bit more closely. :-)
Dec 7, 2017 at 23:14 history edited Iosif Pinelis CC BY-SA 3.0
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Dec 7, 2017 at 22:44 comment added fedja A disadvantage of this definition is that it depends on the choice of the x-axis. I thought so too until I started typing my answer. :-) The real problem is that $\tan x=\tan(\pi+x)$, so sometimes the OP gets the diametrically opposite point to the one he's looking for. However, up to this funny effect the formula is rotation invariant (unbelievable, isn't it?)
Dec 7, 2017 at 22:10 comment added Iosif Pinelis I have modified the previous approach. The new approach is logically simpler. It is also substantially lighter computationally, and it likely has similar (quasi-)optimality properties.
Dec 7, 2017 at 22:04 history edited Iosif Pinelis CC BY-SA 3.0
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Dec 7, 2017 at 17:42 history answered Iosif Pinelis CC BY-SA 3.0