= Pareto highest density interval
{c}
{title2=$[b,b\alpha^{-1/a}]$}
For the <Pareto distribution> of shape $a>0$ and lower bound $b>0$, the density $ab^ax^{-a-1}$ is strictly decreasing on $[b,\infty)$. Its highest-density interval of probability $1-\alpha$, $0<\alpha<1$, must begin at $b$. The tail probability $\mathbb P(X>u)=(b/u)^a$ makes the upper endpoint $u=b\alpha^{-1/a}$. If this is a <posterior distribution>, the result is its <highest posterior density interval>. In particular, <Uniform-Pareto conjugacy> supplies posterior shape $a+n$ and lower bound $\max(b,\max_i y_i)$.
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