= Balanced-panel method-of-moments credibility
{title2=$\widehat a=\max(0,B-\widehat v/n),\quad\widehat Z=n\widehat a/(n\widehat a+\widehat v)$}
For independent comparable risks observed over $n\ge2$ years, estimate the <expected process variance> $v$ by the average within-risk sample variance. The sample variance $B$ of the risk means estimates $a+v/n$, where $a$ is the <variance of hypothetical means>. Thus $B-\widehat v/n$ is unbiased for $a$; truncating at zero produces a practical nonnegative estimate but introduces bias. Use the grand mean for $m$ and plug these estimates into the <Bühlmann credibility premium> $\widehat Z\overline X_s+(1-\widehat Z)\widehat m$. At least two risks are needed for $B$; a single year cannot estimate within-risk variance this way.
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