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) equation

It is convenient to restate (17.1) as

equation

Now let yp be defined by

(17.2) equation

That is, yp 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 yp satisfies

(17.3) equation

Then the condition for full ...

Get Loss Models: From Data to Decisions, 4th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.