\text{NegBinomial}(y~|~\alpha,\beta)  = \binom{y +
\alpha - 1}{\alpha - 1} \, \left( \frac{\beta}{\beta+1}
\right)^{\!\alpha} \, \left( \frac{1}{\beta + 1} \right)^{\!y} \!. \]</span></p>
<p>The mean and variance of a random variable <span class="math inline">\(y \sim \text{NegBinomial}(\alpha,\beta)\)</span> are given by <span class="math display">\[ \mathbb{E}[y] =
\frac{\alpha}{\beta} \ \ \text{ and } \ \ \text{Var}[Y] =
\frac{\alpha}{\beta^2} (\beta + 1). \]</span></p>
</div>
<div id="sampling-statement