Exact Bühlmann credibility for gamma claims
= Exact Bühlmann credibility for gamma claims
{title2=$\widehat m_{\rm B}=\widehat m_{\rm Bayes}$}
With the <gamma scale inverse-gamma conjugacy> model and prior shape $k>2$, the <Bühlmann model> has $v/a=(k-1)/\alpha$. Its <Bühlmann credibility premium> equals $\alpha(\lambda+\sum_jX_j)/(k+n\alpha-1)$, exactly the <Bayes estimator under squared error loss> of $\alpha\Theta$. Equality holds because the <posterior mean> is already affine in the observed <sample mean>.