t is one of the few distributions that are stable and that have probability density functions that can be expressed analytically, the others being the normal distribution and the Cauchy distribution.
In probability theory, a distribution is said to be stable (or a random variable is said to be stable) if a linear combination of two independent copies of a random sample has the same distribution, up to location and scale parameters.
For the Levy Distribution App thtree data parameters for the Location ( a ), the Scale Parameter and a Random Variable ( x ) are input via sliders to compute PDF and CDF values and the Semicircle Distribution mean and variance. The PDF and CDF values are displayed both in data table and graph forms.
The PDF and CDF graphs are touch interactive graphs for computed (x/Pr(x) paired values. The graphs have a touch feature whereby upon the touch a slidable vertical line appears. Upon movement of the line a paired (x,Pr(x) values appear relative to the line position on the graph curve.
The horizontal x-axis displays computed (x) values. The vertical y-axis plots a range of Pr(x) values.
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