I have a question on joint distributions. As an example, say I have two distribution which for this example are normal and I know their mean and variance. I want to find the 99.5th probability of the two distributions combined. I can find the 99.5th percentile for each distribution separately, but the 99.5th percentile for them combined might well allow for some diversification between them.
Lets say they are uncorrelated. Is the correct way to get the 99.5th point of their joint distribution to use a bivariate normal?
If I have more than 2 distributions and some of the marginal distributions are not normal; some might be lognormal, some gamma, some normal; is the correct way to combine them using copulas?
Many thanks for any comments