# Simulating Draws of Multivariate EV-Type Distribution

Let $$\varepsilon = [\varepsilon_1,...,\varepsilon_J]$$ be a random vector that we can partition into $$K$$ disjoint subvectors. $$\varepsilon$$ has this cdf:

$$$$F(\varepsilon) = \exp \bigg[-\sum_{k=1,...,K}\Big ( \sum_{j\in J_k} e^{\varepsilon_j / \gamma} \Big )^ \gamma \bigg].$$$$

This is the distribution of nested logit errors in a discrete choice model, where the elements belonging to the same nest $$k$$ are correlated according to $$\gamma \in [0,1]$$. I need to simulate draws from this distribution but cannot figure out how, without differentiating $$J$$ times and getting the pdf so I can do MCMC.

There is another question here that gives a solution that seems pretty cumbersome for $$J$$ large. And another question here that went unresolved, but maybe the "nice" properties of EV distributions may be helpful?