Random Quantile Experiment

Quantile graph
Distribution graph

Description

This app simulates values from a random variable with a specified special distribution by computing a random quantile. The quantile function of the special distribution is \(F^{-1}\), where \(F\) is the distribution function. If \(U\) has the standard uniform distribution (the uniform distribution on the interval \((0, 1)\)), then \(X = F^{-1}(U)\) has the given special distribution. The graph on the left shows the distribution function/quantile function of the specified distribution, while the graph on the right shows the probability density function. On each run, the value of \(U\) is shown as the horizontal line in the left graph while the value of \(X\) is showns as the vertical line. The values of \(U\) and \(X\) are recorded in the table on the left. As the experiment runs, the empirical density and moments of \(X\) are shown in the right graph and recorded in the right table. the following distributions can be chosen with the selection box:

In each case, the parameters can be set with the input controls.