Extremes of spheroid shape factor based on two dimensional profiles. (English) Zbl 1249.60105

Summary: The extremal shape factor of spheroidal particles is studied. Three dimensional particles are considered to be observed via their two dimensional profiles and the problem is to predict the extremal shape factor in a given size class. We proof the stability of the domain of attraction of the spheroid’s and its profile shape factor under a tail equivalence condition. We show namely that the Farlie-Gumbel-Morgenstern bivariate distribution gives the tail uniformity. We provide a way how to find normalising constants for the shape factor extremes. The theory is illustrated on examples of distributions belonging to Gumbel and Fréchet domain of attraction. We finalyy discuss the ML estimator based on the largest observations, and hence the possible statistical applications.


60G70 Extreme value theory; extremal stochastic processes
62G32 Statistics of extreme values; tail inference
62P30 Applications of statistics in engineering and industry; control charts
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