### Random Quantile Experiment

 Quantile graph Distribution graph

#### Description

This applet 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.