standard for full credibility

How much of your own data is enough to trust it completely? The standard for full credibility is the answer: it is the amount of experience — measured in number of claims, or exposure, or dollars of loss — at which you are willing to set Z = 1 and use your own data alone, ignoring the benchmark. It is the bar you must clear to be 'fully credible'. Below the bar you only get partial credit.

The bar is fixed by two choices made up front. First, how close do you want the estimate to be to the truth (the tolerance, e.g. within plus or minus 5 percent)? Second, how often do you want to be that close (the probability, e.g. 90 percent of the time)? Tighter tolerance or higher confidence both push the required data up. For estimating a Poisson claim frequency to within plus or minus k with probability p, the standard works out to roughly (z-score/k) squared expected claims; the classic '90 percent within 5 percent' choice gives about 1,082 expected claims. If severity also varies, the standard rises to account for that extra noise.

In practice the full-credibility standard is a deliberate, sometimes regulator-blessed convention, not a law of nature — change the tolerance or confidence and the number moves. Its honest limitation is the same as classical credibility's: it is built purely from the variance of your own data and never from how different risks actually are. So 'full credibility' does not mean your data are perfect; it means they are stable enough that the chosen safety target is met.