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c) Relationship to credibility - The process variance and
structure variance also play an important role in credibility
theory. The most general formula for credibility, Z is :
Z=2+2 2

where 2= {Var()} is the structure variance and 2 is
the average process variance. The denominator is the
total variance.

This formula can be derived in another way. Let us have
the claims experience for individual policies in two
different time periods. Without loss of generalization,
we can normalize the loss experience by dividing by the
average cost.

Let xi be the relative cost in the first period and yi be the
relative cost in the second period, for individual policy i.
First we have to determine the credibility Z, to apply to
the loss experience in the first period, in order to most
accurately predict the loss experience in the first period.
In other words,

yi = Zi + (1 - Z)

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