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The function returns the fraction of capacity or demand that matches the allocated amount of a scarce resource given the clearing attractiveness x, the attractiveness a (e.g., utility), and the width w of an extreme value distribution function that describes the priority profile for the recipient.
The parameter w defines a highest density interval (HDI) with a probability of about 0.997 (i.e., the equivalent of a 6σ HDI for a normal probability distribution) that is located around the location parameter a, which in this case denotes the location of the mode of the extreme value distribution. The interval boundaries shown in the graph below are only approximations, but they are close enough for application purposes.
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Functions.allocateExtremeValue(x, a, w);
Functions.allocateExtremeValue(4.25, 5, 3); // 0.9995.. Functions.allocateExtremeValue(5.00, 5, 3); // 0.6321.. Functions.allocateExtremeValue(7.25, 5, 3); // 0.0022..
allocateUniform, allocateTriangular, allocateNormal
encapsulated function allocateExtremeValue import ICON = BusinessSimulation.Icons.Function; extends ICON; input Real x "Clearing attractiveness"; input Real a "Attractiveness of recipient"; input Real w "Width of distribution (i.e., defining a highest density region with probability of 0.997)"; output Real y "Fraction of total capacity or demand allocated to the recipient"; end allocateExtremeValue;