Prediction of the maximum size in wicksell's corpuscle problem, II

Annals of the Institute of Statistical Mathematics

Volumn 53, Issue 3, 2001, Pages 647-660

  Takahashi, Rinya ^a   Sibuya, Masaaki ^b  

^a KOBE UNIVERSITY OF MERCANTILE MARINE   (Japan)

^b Takachiho University   (Japan)

Author keywords

Extreme value theory; Generalized gamma distribution; Gumbel distribution; Metal fatigue; Stereology

Indexed keywords

EID: 6644229999     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014697919230     Document Type: Article

References (14)

1. Hager, H. W. and Bain, L. J. (1970). Inferential procedures for the generalized gamma distribution, J. Amer. Statist. Assoc., 65, 1601-1609.
2. Lawless, J. F. (1980). Inference in the generalized gamma and log gamma distribution, Technometrics, 22, 409-419.
3. Murakami, Y. (1993). Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions, Yokendo, Tokyo (in Japanese).
4. Murakami, Y. (1994). Inclusion rating by statistics of extreme values and its application to fatigue strength prediction and quality control of materials, Journal of Research of the National Institute of Standards and Technology, 99, 345-351.
5. Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed. Wiley, New York.
6. Sibuya, M. (1984). Unimodal hazard functions, Japanese Journal of Applied Statistics, 13, 115-124 (in Japanese).
7. Sibuya, M. (1999). Wicksell's corpuscle problem, Encyclopedia of Statistical Sciences: Update Vol. 3 (eds. S. Kotz, C. Read and D. L. Bankd), 809, Wiley, New York.
8. Stacy, E. W. and Mihram, G. A. (1965). Parameter estimation for a generalized gamma distribution, Technometrics, 7, 349-358.
9. Stuart, A. and Ord, J. K. (1987). Kendall's Advanced Theory of Statistics, Vol. 1, 5th ed., Griffin, London.
10. Takahashi, R. and Sibuya, M. (1996). The maximum size of the planar sections of random spheres and its application to metallurgy, Ann. Inst. Statist. Math., 48, 127-144.
11. Takahashi, R. and Sibuya, M. (1998). Prediction of the maximum size in Wicksell's corpuscle problem, Ann. Inst. Statist. Math., 50, 361-377.
12. Takahashi, R., Nawata, S. and Sibuya, M. (1996). Wicksell inverse transformation: An ill-posed problem, Japanese Journal of Applied Statistics, 25, 121-142 (in Japanese).
13. Takahasi, H. and Mori, M. (1974). Double exponential formulas for numerical integration, Pub. Res. Inst. Math. Sci., 9, 721-741.
14. Wicksell, S. D. (1925). The corpuscle problem. A mathematical study of a biometric problem, Biometrika, 17, 84-99.