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Consider the situation when you have two expressions with the same distribution. Is there any standard notation to express they have the same distribution?

An example: $U$ is uniformly distributed on $(0,2\pi)$, then $\cos(U)$ has the same distribution as $\sin(U)$. What is the cleanest, most intuitive way to express this mathematically?

I meant $\text{dist}(\cos(U)) = \text{dist}(\sin(U))$, but I assume there is something more standard.

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  • $\begingroup$ dist is by default for distance (though there, you'd obviously have 2 arguments). $\endgroup$
    – Batman
    May 22, 2017 at 21:31
  • $\begingroup$ @Batman Yes, I know, but it wouldn't be the first occasion of ambiguous terminology on different fields. $\endgroup$
    – plasmacel
    May 22, 2017 at 21:36

1 Answer 1

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Notation : $\cos(U) \stackrel d=\sin(U)$

If $X$ and $Y$ follow same distribution then mathematically you can write $X \stackrel d=Y$.

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