Interval Estimation Under The Uniform Distribution U(a,b)

In this short note, we consider interval estimation for the parameters under the uniform distribution U(a, b). We study two approaches: (1) based on a Wald-type statistic, (2) based on a pivotal statistic. We show that the first approach in its common form is not valid and we propose a modified version of the first approach. It turns out it is equivalent to the confidence interval with the shortest length.