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Let's say X is uniformly distributed in [-1 , 1]

Then what can we call the distribution of X³ ? It is not uniform, but it "mirrors" around 0 as well.

Is there a simple word describing X³ that would also apply to X⁵ and to 3X, for example?

I would call it "mirror around zero" but I find this ugly and was wondering if there's a better and established term.

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    $\begingroup$ Saying the distribution is "symmetric" about 0 is probably the best you can do with one word. This implies that 0 is the median, but it is a stronger condition than merely requiring 0 to be the median. $\endgroup$
    – hardmath
    Jan 25, 2015 at 4:20
  • $\begingroup$ Good suggestion, it fits perfectly for my use case. Thanks! $\endgroup$
    – user985366
    Jan 25, 2015 at 4:25

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Per the OP's comment, saying the distribution is "symmetric about zero" is a suitable phrase.

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