Is there a standard well-known notation for approximation of a distribution?
If a random variable $X$ has exactly standard normal distribution then we write $X \sim \mathcal {N}(0,1)$.
But what symbol should we use instead of "$\sim$" when the real distribution is unknown and we know only its approximation?
For example, sample mean $\overline{X} = \frac{1}{n}\sum_{i=1}^n X_i$ has approximately normal distribution $\mathcal{N}(\mu, \frac{\sigma^2}{n})$ when $n$ is large enough. I saw that some sources use symbol "$\approx$" in the following way: $\,\,\overline{X} \approx \mathcal{N}(\mu, \frac{\sigma^2}{n})$. But I'm not sure that symbol "$\approx$" is a standard well-known notation for approximation of a distribution.
Instead of stacking together two tildes, you could put a dot above and a dot below the tilde to indicate an approximate distribution(similar to a notation for approximate equal with a dot above and below an equal sign), as shown below:
$\overset{\lower{0.5ex}{\cdot}}{\underset{\raise{1ex}{\cdot}}{\sim}}$.