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In statistics notation, the tilde is often used to indicate "has the distribution of," as in $X \sim N(0,1)$, meaning the random variable $X$ follows the distribution of the standard normal distribution.

What does it mean when the letter (variable?) $a$ is set above the tilde operator, as in $Z\overset{a}{\sim}\operatorname{normal}(\mu,\sigma^2)$? I suppose the $a$ has a function similar to the dot in $\mathrel{\dot\sim}$ (see What exactly does $\dot\sim$ notation mean?), but I'm not finding it.

Mike Chapman
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    I would guess [*asymptotically distributed as*](https://en.wikipedia.org/wiki/Asymptotic_distribution) – Henry May 17 '18 at 22:59
  • Another possibility is "approximately distributes as" – kjetil b halvorsen May 17 '18 at 23:06
  • I feel sheepish, I found the explanation in the work I was referring to: “where $\overset{a}{\sim}$ is read ‘approximately distributed as,’” the exact same as $\mathrel{\dot\sim}$ linked above. So in this context, halvorsen guessed the right possibility. I should have searched more carefully, but hopefully the question will still be a useful reference for somebody in future. The reference in question is https://tbrieder.org/epidata/course_reading/e_tableman.pdf (see p. 25). Unfortunately, I can't upvote comments yet. – Mike Chapman May 18 '18 at 07:48
  • I actually found a second explanation in the work: “$\overset{a}{\sim}$ is read ‘is asymptotically distributed,’” on p. 57. So in fact, both of you guessed the right possibility, and it's necessary to pay close attention to the context. Thanks to both commenters. – Mike Chapman May 18 '18 at 08:08

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