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We introduce a general method, named the h-function method, to unify theconstructions of level-alpha exact test and 1-alpha exact confidence interval.Using this method, any confidence interval is improved as follows: i) anapproximate interval, including a point estimator, is modified to an exactinterval; ii) an exact interval is refined to be an interval that is a subsetof the previous one. Two real datasets are used to illustrate the method.

A Unified Approach for Constructing Confidence Intervals and Hypothesis Tests Using h-function