Uniform Estimation Experiment

Description

The experiment is to generate a random sample \(\boldsymbol{X} = (X_1, X_2, \ldots, X_n)\) from the uniform distribution on the interval \([0, a]\). The statistics of interest are \begin{align} U & = \frac{2}{n} \sum_{i=1}^n X_i \\ V & = \frac{n+1}{n} \max\{X_1, X_2, \ldots, X_n\} \\ W & = (n + 1) \min\{X_1, X_2, \ldots, X_n\} \end{align} Each statistic is a point estimator of \(a\). The parameters \(a\) and \(n\) can be varied with the input controls.