Loss Models: From Data to Decisions, 4th Edition

17.3 Full credibility

One method of quantifying the stability of is to infer that is stable if the difference between and ξ is small relative to ξ with high probability. In statistical terms, stability can be defined by selecting two numbers r > 0 and 0 < p < 1 (with r close to 0 and p close to 1, common choices being r = 0.05 and p = 0.9) and assigning full credibility if

(17.1)

It is convenient to restate (17.1) as

Now let y_p be defined by

(17.2)

That is, y_p is the smallest value of y that satisfies the probability statement in braces in (17.2). If has a continuous distribution, the “≥” sign in (17.2) may be replaced by an “=” sign, and y_p satisfies

(17.3)

Then the condition for full ...