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Extreme Value Distribution

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Extreme Value Distribution

In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. By the extreme value theorem the GEV distribution is the only possible limit distribution of properly normalized maxima of a sequence of independent and identically distributed random variables. Extreme value distributions are the limiting distributions for the minimum or the maximum of a very large collection of random observations from the same arbitrary distribution.

For the Extreme Value Distribution App three data parameters for the Location ( μ ), Scale ( σ ) and (x) Variable are input via sliders to compute PDF and CDF values and the Erlang 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.
Donald Schaefer