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

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

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?

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