risk - Parametric/Analytical VaR

Suppose I want to calculate VaR for a known distribution with mean $\mu$, variance $\sigma^2$ and $\alpha$-quantile as, $VaR_{\alpha}$ = $\mu + \sigma q_{\alpha}$.

For a Gaussian distribution it is clear that $q_{\alpha}=z_{\alpha}$ where $z_{\alpha}$ is the $\alpha$-quantile of a standard normal distribution with $\mu,\sigma$ being the moments.

Now I have two questions

1. 
   
   

   For returns with student-t distribution, there can be two ways to calculate VaR. First, use moment definition of student-t and standard t quantile. This gives an unbiased estimate for VaR. Second, use moment definition of student-t and quantile from standard normal distribution. This is a biased estimate for VaR. How does one understand which VaR is used most non-normal definitions of VaR are loosely defined in that sense.

   
   


2. 
   

   For parametric distributions which are defined using location and scale such as Azzalini's skew-t, where mean and standard deviation are different from location and scale there can be three definitions of VaR. First, use moment definition of skew-t and standard skew-t quantile. This gives an biased estimate for VaR. Second, use moment definition of skew-t and quantile from standard normal distribution. This is a biased estimate for VaR. Third, define VaR using location, scale and standard skew-t quantile. This gives an unbiased estimate. How does one name and distinguish the three cases to avoid any ambiguity.

   
   

In general the challenge in defining VaR is which moments to use and which quantile should be used. Are there any references that elaborate on using parametric VaR for non-normal distributions