Title: Applications of the Fréchet distribution function

Authors: D. Gary Harlow

Addresses: Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015-3085, USA

Abstract: The Fréchet cumulative distribution function (CDF) is the only CDF defined on the nonnegative real numbers that is a well-defined limiting CDF for the maxima of random variables (RVS). Thus, the Fréchet CDF is well suited to characterize RVS of large features. As such, it is important for modelling the statistical behaviour of materials properties for a variety of engineering applications. Since the Fréchet CDF is not commonly used, some of its properties are reviewed. Parametric estimation using both graphical and maximum likelihood methods are considered. Two examples, modelling interfacial damage in microelectronic packages and material properties of constituent particles in an aluminium alloy, are given. A third example is considered in which truncation in the upper tail is suggested. The Fréchet CDF is recommended as a viable statistical model.

Keywords: constituent particles; Fréchet cumulative distribution function; CDF; interfacial damage; material properties; maximum likelihood estimation; microelectronics; statistical estimation; truncated Fréchet distribution function; aluminium alloys.

DOI: 10.1504/IJMPT.2002.005472

International Journal of Materials and Product Technology, 2002 Vol.17 No.5/6, pp.482 - 495

Published online: 11 Oct 2004 *

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