span> Negative Binomial Distribution (log alternative parameterization)</h2>
<p>Related to the parameterization in section <a href="nbalt.html#nbalt">negative binomial, alternative parameterization</a>, the following
parameterization uses a log mean parameter <span class="math inline">\(\eta = \log(\mu)\)</span>, defined
for <span class="math inline">\(\eta \in \mathbb{R}\)</span>, <span class="math inline">\(\phi \in \mathbb{R}^+\)</span>, so that for <span class="math inline">\(n \in \mathbb{N}\)</span>, 