nds to the maximum of the
weighted corresponding entry. That is, <span class="math inline">\(X_{i}=\max_{b \in \mathbb{B}_d}\theta_{i,
b}Z_{i,b}\)</span> for all <span class="math inline">\(i=1, \ldots,
d\)</span>. The max-mixture is valid provided that <span class="math inline">\(\sum_{b
\in \mathbb{B}_d} \theta_{i,b}=1\)</span> for <span class="math inline">\(i=1, \ldots, d.\)</span> As such, empirical
estimates of the spectral measure will almost surely place mass on the
inside of the simplex rather than