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I am reading a paper and it has a bit of mathematical notation that I need help with. I don't have a mathematics background therefore, I would really appreciate it if someone can help me with it. The formula is :

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Can someone explain what ';' means in this formula. NB simply refers to negative binomial. Help would be appreciated.

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    $\begingroup$ Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures. $\endgroup$
    – José Carlos Santos
    Apr 12, 2020 at 8:39

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I assume $\hat{x}$ is the mean and $\theta$ the standard deviation, so '$;$' in this context means 'with', 'given' or 'such that', similar to the vertical bar '$|$'.

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  • $\begingroup$ Thanks. It makes much more sense to me now. $\endgroup$
    – John
    Apr 12, 2020 at 11:30
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This looks like a likelihood function to me, but is hard to tell without any additional clarification what the notation means. Some people use ; to distinguish between the observed outcomes (which are constants in the likelihood function) and the parameters of the probability distribution (the variables of the likelihood function). For example if we observe a sample $x\in\mathbb{R}^n$ of size $n$ from a normal distribution, then we could denote the corresponding likelihood function as $L(\mu,\sigma^2;x)$.

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