# Needs clarity with notations

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 :

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

• Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures. Apr 12, 2020 at 8:39

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 '$$|$$'.
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 $$L(\mu,\sigma^2;x)$$.