Distributed to symbol for frequency distributions

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How would you write down that some random variable $X$ is distributed to a frequency distribution.

For the normal distribution e.g. I often see sth. like that: $X\sim \mathcal{N}(\mu,\sigma^2)$. Is it ok to write $X\sim \mathcal{H}$ with $\mathcal{H}$ as the frequency distribution?