The generalized FGM distribution and its application to stereology of extremes

Daniel Hlubinka; Samuel Kotz

Applications of Mathematics (2010)

  • Volume: 55, Issue: 6, page 495-512
  • ISSN: 0862-7940

Abstract

top
The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.

How to cite

top

Hlubinka, Daniel, and Kotz, Samuel. "The generalized FGM distribution and its application to stereology of extremes." Applications of Mathematics 55.6 (2010): 495-512. <http://eudml.org/doc/116487>.

@article{Hlubinka2010,
abstract = {The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.},
author = {Hlubinka, Daniel, Kotz, Samuel},
journal = {Applications of Mathematics},
keywords = {generalized FGM distribution; extremes; stereology; maximum domain of attraction; extremes; stereology; maximum domain of attraction},
language = {eng},
number = {6},
pages = {495-512},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The generalized FGM distribution and its application to stereology of extremes},
url = {http://eudml.org/doc/116487},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Hlubinka, Daniel
AU - Kotz, Samuel
TI - The generalized FGM distribution and its application to stereology of extremes
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 6
SP - 495
EP - 512
AB - The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.
LA - eng
KW - generalized FGM distribution; extremes; stereology; maximum domain of attraction; extremes; stereology; maximum domain of attraction
UR - http://eudml.org/doc/116487
ER -

References

top
  1. Bairamov, I., Kotz, S., 10.1007/s001840100158, Metrika 56 (2002), 55-72. (2002) MR1922211DOI10.1007/s001840100158
  2. Bairamov, I., Kotz, S., Bekçi, M., 10.1080/02664760120047861, J. Appl. Stat. 28 (2001), 521-536. (2001) MR1836732DOI10.1080/02664760120047861
  3. Bairamov, I., Kotz, S., Gebizlioglu, O. L., The Sarmanov family and its generalization, S. Afr. Stat. J. 35 (2001), 205-224. (2001) Zbl1009.62011MR1910896
  4. Beneš, V., Bodlák, K., Hlubinka, D., 10.1023/A:1026283103180, Methodol. Comput. Appl. Probab. 5 (2003), 289-308. (2003) Zbl1041.62039MR2016768DOI10.1023/A:1026283103180
  5. Beneš, V., Jiruše, M., Slámová, M., 10.1016/S1359-6454(96)00249-2, Acta Materialia 45 (1997), 1105-1197. (1997) DOI10.1016/S1359-6454(96)00249-2
  6. Coles, S., An Introduction to Statistical Modeling of Extreme Values, Springer London (2001). (2001) Zbl0980.62043MR1932132
  7. Cruz-Orive, L. M., 10.1111/j.1365-2818.1976.tb02446.x, J. Microscopy 107 (1976), 235-253. (1976) DOI10.1111/j.1365-2818.1976.tb02446.x
  8. Dress, H., Reiss, R.-D., Tail behavior in Wicksell's corpuscle problem, In: Probability Theory and Applications J. Galambos, J. Kátai Kluwer Dordrecht (1992), 205-220. (1992) Zbl0767.60008MR1211909
  9. Embrechts, P., Klüppelberg, C., Mikosch, T., Modelling Extremal Events for Insurance and Finance. Applications of Mathematics. 33, Springer Berlin (1997). (1997) MR1458613
  10. Gnedenko, B. V., 10.2307/1968974, Ann. Math. 44 (1943), 423-453. (1943) Zbl0063.01643MR0008655DOI10.2307/1968974
  11. Hlubinka, D., Extremes of spheroid shape factor based on two dimensional profiles, Kybernetika (to appear). MR2208521
  12. Hlubinka, D., 10.1023/A:1026234329084, Extremes 6 (2003), 5-24. (2003) Zbl1051.60011MR2021590DOI10.1023/A:1026234329084
  13. Hlubinka, D., Stereology of extremes; size of spheroids, Math. Bohem. 128 (2003), 419-438. (2003) Zbl1053.60053MR2032479
  14. Hlubinka, D., Bivariate models for extremes in stereology, Tech. Rep., KPMS, Charles University in Prague (2005). (2005) MR2021590
  15. Johnson, N. L., Kotz, S., 10.1080/03610927508827258, Commun. Stat. 4 (1975), 415-427. (1975) Zbl0342.62006MR0373155DOI10.1080/03610927508827258
  16. Nelsen, R. B., 10.1007/978-1-4757-3076-0_1, Springer New York (1999). (1999) MR1653203DOI10.1007/978-1-4757-3076-0_1
  17. Ohser, J., Mücklich, F., Statistical Analysis of Microstructures in Materials Science, Wiley Chichester (2000). (2000) 
  18. Rodríguez-Lallena, J. A., Úbeda-Flores, M., 10.1016/j.spl.2003.09.010, Stat. Probab. Lett. 66 (2004), 315-325. (2004) Zbl1102.62054MR2045476DOI10.1016/j.spl.2003.09.010
  19. Takahashi, R., Sibuya, M., 10.1007/BF00049294, Ann. Inst. Stat. Math. 48 (1996), 127-144. (1996) Zbl0864.60010MR1392521DOI10.1007/BF00049294
  20. Takahashi, R., Sibuya, M., 10.1023/A:1003451417655, Ann. Inst. Stat. Math. 50 (1998), 361-377. (1998) Zbl0986.62075MR1868939DOI10.1023/A:1003451417655
  21. Takahashi, R., Sibuya, M., 10.1023/A:1014697919230, Ann. Inst. Stat. Math. 53 (2001), 647-660. (2001) Zbl1078.62525MR1868897DOI10.1023/A:1014697919230
  22. Takahashi, R., Sibuya, M., 10.1023/A:1020982025786, Extremes 5 (2002), 55-70. (2002) MR1947788DOI10.1023/A:1020982025786
  23. Takahashi, R., Sibuya, M., 10.1002/asmb.477, Appl. Stoch. Models Bus. Ind. 18 (2002), 301-312. (2002) Zbl1010.62113MR1932643DOI10.1002/asmb.477
  24. Weissman, I., Estimation of parameters and large quantiles based on the k largest observations, J. Am. Stat. Assoc. 73 (1978), 812-815. (1978) Zbl0397.62034MR0521329
  25. Wicksell, S. D., The corpuscle problem I. A mathematical study of a biometric problem, Biometrika 17 (1925), 84-99. (1925) 
  26. Wicksell, S. D., The corpuscle problem II, Biometrika 18 (1926), 152-172. (1926) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.