For a scientific publication I am documenting the algorithm of my computer model. The model uses the Monte Carlo method and has some random variables input. Now I would like to document that correctly.
So for instance variable $a$ is determined by multiplying variable $b$ with a random number $X$, which is drawn from a log-normal probability density function. My guess for a notation would be as follows:
$a_{i} = b_{i} \cdot X_{i}, \quad X_{i} \sim \ln \mathcal{N}(\mu_{i}, \sigma_{i}^{2})$
But I ask myself:
- Is this $\LaTeX$ notation correct (use of comma,
\quad
, $\ln\mathcal{N}$) as an equation in a publication? - What is a typical random variable symbol? $X$ seems to be quite common.
- How can I document other distributions, such as Weibull, log-logistic, discrete uniform?