Applications of the Fréchet distribution function

The Frechet 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 Frechet 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 Frechet 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 Frechet CDF is recommended as a viable statistical model.