= Credibility estimate
{title2=$\widehat\mu=Z\overline X+(1-Z)\mu$}
A <credibility estimate> combines a risk's individual experience with population information. In the basic equal-exposure form, the <credibility factor> $Z$ weights the observed <sample mean>, while $1-Z$ weights a prior or collective <expected value>. The <Bühlmann credibility premium> is the best affine estimate under <mean squared error>; an exact <Bayesian posterior> mean can also have this form, as in the <natural conjugate credibility identity>.
Back to article page
