Abstract
Confidence intervals for any power of a scale parameter of a distribution are constructed. We first state the needed general distributional assumptions and show how to construct the minimum length location-scale invariant interval, having a predetermined coverage coefficient 1− α. If we then relax the invariance restriction, we obtain an improved interval. Using information relating the size of the location parameter to that of the scale parameter, we shift the minimum length interval closer to zero, simultaneously bringing the endpoints closer to each other. These intervals have guaranteed coverage probability uniformly greater than a predetermined value 1− α, and have uniformly shorter length than the shortest location scale invariant interval. We illustrate our method with some examples.
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