Statistical Inferences on Uniform Distributions: The Cases of Boundary Values Being Parameters

If a continuous random variable X is uniformly distributed over the interval and if any of the two boundary values is unknown, it is necessary to make inferences related to the unknown parameter. In this work, for the unknown boundary values of X, some unbiased estimators based on certain order statistics and sample mean are suggested. These estimators are compared in terms their efficiencies. The most efficient unbiased estimator is used to provide confidence intervals and tests of hypotheses procedures for the unknown parameter (the unknown boundary value).