ixture of the log densities lp1 and lp2 with mixing
proportion theta, defined by <span class="math display">\[\begin{eqnarray*}
\mathrm{log\_mix}(\theta, \lambda_1, \lambda_2) &amp; = &amp; \log \!\left(
\theta \exp(\lambda_1) + \left( 1 - \theta \right) \exp(\lambda_2)
\right) \\[3pt] &amp; = &amp; \mathrm{log\_sum\_exp}\!\left(\log(\theta) +
\lambda_1, \ \log(1 - \theta) + \lambda_2\right). \end{eqnarray*}\]</span></p>
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<p><code>real</code> <strong><cod