Abstract
An interesting topic in mathematical statistics is that of constructing confidence intervals. Two types of intervals, both based on the method of pivotal quantity, are available: the Shortest Confidence Interval (SCI) and the Equal Tails Confidence Interval (ETCI). The aims of this article are: (i) to clarify and comment on methods of finding such intervals; (ii) to investigate the relationship between these types of intervals; (iii) to point out that confidence intervals with the shortest length do not always exist, even when the distribution of the pivotal quantity is symmetric; and finally, (iv) to give similar results when the Bayesian approach is used.
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