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


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 ...

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