Shape factor extremes for prolate spheroids. (English) Zbl 1249.60106
Summary: Microscopic prolate spheroids in a given volume of an opaque material are considered. The extremes of the shape factor of the spheroids are studied. The profiles of the spheroids are observed on a random planar section, and, based on these observations, we estimate the distribution of the extremal shape factor of the spheroids. We show that under a tail uniformity condition, the Maximum domain of attraction is stable. We discuss the normalising constants (n.c.) for the extremes of the spheroid and profile shape factor. Comparing the tail behaviour of the distribution of the profile and the spheroid shape factor, we show the relation between the n.c. of the profile shape factor (which can be estimated) and the n.c. of the spheroid shape factor (cannot be estimated directly) which are needed for the prediction of the tail behaviour of the shape factor. The paper completes our study in the paper [Kybernetika 42, No. 1, 77–94 (2006; Zbl 1249.60105)] for prolate spheroids.
MSC:
| 60G70 | Extreme value theory; extremal stochastic processes |
| 62G32 | Statistics of extreme values; tail inference |
| 62P30 | Applications of statistics in engineering and industry; control charts |
Citations:
Zbl 1249.60105Software:
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