inline">\(\sum_{b \in \mathbb{B}_d} \theta_{i, b}
=1\)</span> for <span class="math inline">\(i=1, \ldots, d\)</span>; the
distribution function is <span class="math display">\[\begin{align*}
\Pr(\boldsymbol{X} \le \boldsymbol{x}) = \exp \left[ -\sum_{b \in
\mathbb{B}_d}(-1)^{|b|}
\left\{\sum_{i \in b}
\left(\frac{\theta_{i,
b}}{x_i}\right)^{\alpha_b}\right\}^{\frac{1}{\alpha_b}}\right].
\end{align*}\]</span> In particular, it does not correspond to the
``negative logistic distribution’’ given in e.g., 