Uniform Estimation Experiment

Distribution graph


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 probability density function of the distribution is shown in blue in the graph, and on each update, the sample density function is shown in red.On each update, the following statistics are recorded: \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 theoretical bias and mean square error of each estimator is shown in the table for that estimator. On each update, the empirical bias and mean square error are recorded in the tables. The parameters \(a\) and \(n\) can be varied with the input controls.