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I was wondering if the symbol $\not\sim$ (i.e., not tilde) could be used to express that a random variable $X$ is not distributed as a normal distribution with a mean of $0$ and variance of $1$. For instance, is this appropriate: $$X\not\sim N(0,1)$$

Or is it more common to say: $$X \text{ is not } X\sim N(0,1)$$

I need a way to express it in a symbolic form to be as succinct as possible. Any help would be greatly appreciated.

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    $\begingroup$ I think the most common way would be to just use words $\endgroup$ Commented Mar 6, 2019 at 3:47

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I have never seen anyone say this, but that first notation seems to have an obvious meaning to me, so I would think that is a perfectly reasonable way to write this. (The second notation seems flawed to me, since it says "$X \text{ is not }X$" which is a contradiction.)

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