Uncunx Java Applet, by Jeffrey S. Rosenthal, August 2009

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This applet simulates an "uncunx" (a modification of the standard "quincunx" device) for illustrating probability distributions. Instead of nails, the balls are deflected by triangles whose width can be adjusted by the user. For some choices of widths, the limiting distribution is still approximately normal, while for others it is far from normal.

The applet accepts the following keyboard inputs (you may need to "click" on the applet first): press 'P' to pause/unpause the simulation, or 'F' and 'S' to go faster/slower, or 'R' to restart, or 'Z' to zero the histogram counts, or 'I' to re-initialise. Or, click your mouse on the '+' and '-' boxes to increase/decrease the widths of the corresponding triangles. Or, press 'D' to instead choose the widths iid randomly.

Alternatively, you may press 'Q' to enter "quantile" mode or, once in quantitle mode, to cycle through four different non-normal distributions [Gamma(2,1), Gamma(4,1), exponential, lognormal] before returning to normal mode. In quantile mode, the uncunx simulates the specified non-normal distribution by setting the triangle widths such that at the i'th row, the ball reaches a quantile corresponding to an odd multiple of 2^{-i}.

Pedagogical uses of the uncunx are described in the recent paper Beyond the Quintessential Quincunx, by M.A. Proschan and J.S. Rosenthal (American Statistician 64:78-82, 2010).

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