caa a22 4500 477062733 CHVBK 20180405111405.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00049294 doi (NATIONALLICENCE)springer-10.1007/BF00049294 The maximum size of the planar sections of random spheres and its application to metallurgy [Elektronische Daten] [Rinya Takahashi, Masaaki Sibuya] A theorem of this paper proves that if the size distribution of random spheres is generalized gamma, its Wicksell transform and other related distributions belong to the domain of attraction of the Gumbel distribution. The theorem also shows the attraction coefficients of the distributions. The fatigue strength of high-strength steel is closely related to the maximum size of nonmetallic inclusions in the region of maximum stress of the steel. Murakami and others developed a method, making use of the Gumbel QQ-plot, for predicting the maximum size from the size distribution of inclusion circles in microscopic view-fields. Based on the Gumbel approximation of the maximum of wicksell transforms, a modified and extended version of Murakami's method is justified, and its performance is evaluated by simulation. The Institute of Statistical Mathematics, 1996 Extreme value theory nationallicence generalized gamma distribution nationallicence Gumbel distribution nationallicence metal fatigue nationallicence stereology nationallicence Wicksell's corpuscle problem nationallicence Takahashi Rinya Kobe University of Mercantile Marine, 5-1-1, Fukae-Minami, Higashi-Nada-ku, 658, Kobe, Japan aut Sibuya Masaaki Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, 223, Yokohama, Japan aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 127-144 0020-3157 48:1<127 1996 48 10463 https://doi.org/10.1007/BF00049294 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049294 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Takahashi Rinya Kobe University of Mercantile Marine, 5-1-1, Fukae-Minami, Higashi-Nada-ku, 658, Kobe, Japan aut NATIONALLICENCE 700 1- Sibuya Masaaki Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, 223, Yokohama, Japan aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 127-144 0020-3157 48:1<127 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer