# Convolution of Dependent Random Variables with Copulas

Lets say I have 2 different observations which are fitted to a parametric distribution. And lets say that they are dependent and can be modeled by one of the copulas. I want to calculate “a value” that is sum of “a possible value from the first distribution” and “a possible value from the second distribution” which their jointly exist with %99 probability.

Lets say I have 1000 observations that are distributed between (100 ~ 400) and fitted to an Extreme Value Distribution and another observation also EVT distributed between (200 ~ 600). Assume that their maximals are dependent and modeled by a Gumbel copula.

What I want to fetch that for example for %99 of chance, their sum will be 1050 (even their maximum observations were 400 and 600 which would yield to 1000). Since they are fitted to an EVT distribution, there is a possibility to be observed higher values than 400 and 600 in the near future.

From what I understand, Copula can give me the joint probability, but how can I tell the copula that give me a couple which their jointly happening probability would be 0.99 ? On normal parametric distributions we can do that by using Inverse CDF function, but copulas do not have inverse CDF or etc. I'm basically stuck.

• See my last comment to your question, maybe it helps. May 8 '19 at 22:11