APPENDIX D SHORTEST COVERAGE INTERVAL FOR MONTE CARLO METHOD
In Section 3-4.1, the methodology is given for determining coverage intervals for Monte Carlo Method (MCM) simulations when the distribution of the results is asymmetric. The approach shown is the probabilistically symmetric coverage interval. The GUM supplement [1] provides an alternative coverage interval for MCM simulations called the “shortest coverage interval.” This interval is the shortest among all possible intervals for a distribution of MCM results where each interval has the same coverage probability. The concept is illustrated in Figure D.1.
Figure D.1 Concept for determining shortest coverage interval for a 100p% level of confidence.
For a distribution of M Monte Carlo results, there can be (1 − p)M intervals that contain 100p% of the total number of results. In Figure D.1, we show the first interval, which starts with sorted result 1, and the last interval, which ends with sorted result M. For instance, if we wanted a 95% level of coverage,
(D.1)
where p = 0.95 for 95% coverage and the last interval would be
(D.2)
The other intervals would be
(D.3)
(D.4)
and so on. The interval with the smallest value ...
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