Actuarial credibility
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Actuarial credibility is a technique used by actuaries to smooth estimates. It is closely related to Bayesian methods in statistics. In a typical application, the actuary has an estimate X based on a small set of data, and an estimate M based on a larger but not-quite-as relevant set of data. The credibility estimate is ZX + (1-Z)M. Z is a number between 0 and 1, calculated to best balance the noisiness of X against the lack of relevance (and noisiness) of M.
For example, an actuary has accident and payroll historical data for a shoe factory that suggest that the accident rate is 3.1 accidents per million dollars of payroll. She has industry statistics (based on all shoe factories) suggesting that the rate is 7.4 accidents per million. With a credibility, Z, of 30%, she would estimate the rate for the factory as 30%(3.1) + 70%(7.4) = 6.1 accidents per million.
[edit] Sources
Whitney, A.W. (1918) The Theory of Experience Rating, Proceedings of the Casualty Actuarial Society, 4, 274-292 [This is one of the original casualty actuarial papers dealing with credibility. It uses Bayesian techniques, although the author uses the now archaic "inverse probability" terminology.]
Longley-Cook, L.H. (1962) An introduction to credibility theory PCAS, 49, 194-221.
