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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.

Graph of the allocateExtremeValue Function (Distribution Shown Scaled for Clarity)

Syntax

Functions.allocateExtremeValue(x, a, w);

Examples

Functions.allocateExtremeValue(4.25, 5, 3); // 0.9995..
Functions.allocateExtremeValue(5.00, 5, 3); // 0.6321..
Functions.allocateExtremeValue(7.25, 5, 3); // 0.0022..

See also

allocateUniform, allocateTriangular, allocateNormal

y = allocateExtremeValue(x, a, w)

x	Type: Real Description: Clearing attractiveness
a	Type: Real Description: Attractiveness of recipient
w	Type: Real Description: Width of distribution (i.e., defining a highest density region with probability of 0.997)

y	Type: Real Description: Fraction of total capacity or demand allocated to the recipient

• Introduced in v2.0.0.