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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.

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    $\begingroup$ I would guess asymptotically distributed as $\endgroup$
    – Henry
    Commented May 17, 2018 at 22:59
  • $\begingroup$ Another possibility is "approximately distributes as" $\endgroup$
    – kjetil b halvorsen ♦
    Commented May 17, 2018 at 23:06
  • $\begingroup$ 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 tbrieder.org/epidata/course_reading/e_tableman.pdf (see p. 25). Unfortunately, I can't upvote comments yet. $\endgroup$
    – Mike Chapman
    Commented May 18, 2018 at 7:48
  • $\begingroup$ 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. $\endgroup$
    – Mike Chapman
    Commented May 18, 2018 at 8:08

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