Recognition of stable distribution with Lévy index α close to 2

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 5, 2012, Pages

  Burnecki, Krzysztof ^a   Wyłomańska, Agnieszka ^a   Beletskii, Aleksei ^b   Gonchar, Vsevolod ^b   Chechkin, Aleksei ^b,c  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b KHARKOV INSTITUTE OF PHYSICS AND TECHNOLOGY   (Ukraine)

^c UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICS; EMPIRICAL PROBABILITIES; EXPERIMENTAL DATA; FUSION DEVICES; GAUSSIAN FLUCTUATIONS; GAUSSIANS; HIGH CONFINEMENT; L-H TRANSITION; L-MODES; POTENTIAL FLUCTUATIONS; SAMPLE SIZES; SIMULATED DATA; STABLE DISTRIBUTIONS; TESTING PROCEDURE; TURBULENT PLASMAS;

FUSION REACTORS; PLASMA TURBULENCE; STATISTICAL TESTS;

PLASMA DENSITY;

EID: 84862023306     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.056711     Document Type: Article

References (47)

1. P. P. Lévy, Calcul des Probabilités (Gauthier Villars, Paris, 1925);
2. Théorie del'addition des Variables Aléatoires, 2nd ed. (Gauthier Villars, Paris, 1937).
3. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions of Sums of Independent Random Variables (Addison-Wesley, Cambridge, 1954).
4. V. M. Zolotarev, One-Dimensional Stable Distributions (American Mathematical Society, Providence, 1986) (Russian edition: Nauka, Moscow, 1983).
5. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes (Chapman and Hall, New York, 1994).
6. A. Janicki and A. Weron, Simulation and Chaotic Behavior of α -Stable Stochastic Processes (Marcel Dekker, New York, 1994).
7. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2 (Wiley, New York, 1971).
8. V. V. Uchaikin and V. M. Zolotarev, Chance and Stability (VSP Press, Utrecht, 1999).
9. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000).
10. A. Chechkin, R. Metzler, J. Klafter, and V. Gonchar, in Anomalous Transport: Foundations and Applications, edited by, R. Klages, G. Radons, and, I. Sokolov, (Wiley-VCH, Weinheim, 2008).
11. R. Metzler, A. V. Chechkin, and J. Klafter, in Encyclopedia of Complexity and System Science, edited by, R. A. Mayers, (Springer-Verlag, Berlin, 2008), Article 293.
12. D. Brockmann, L. Hufnagel, and T. Geisel, Nature (London) NATUAS 0028-0836 10.1038/nature04292 439, 462 (2006). (Pubitemid 43152835)
13. P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature (London) NATUAS 0028-0836 10.1038/nature06948 453, 495 (2008). (Pubitemid 351733320)
14. D. W. Sims, E. J. Southall, N. E. Humphries, G. C. Hays, C. J. A. Bradshaw, J. W. Pitchford, A. James, M. Z. Ahmed, A. S. Brierley, M. A. Hindell, D. Morritt, M. K. Musyl, D. Righton, E. L. C. Shepard, V. J. Wearmouth, R. P. Wilson, M. J. Witt, and J. D. Metcalfe, Nature (London) NATUAS 0028-0836 10.1038/nature06518 451, 1098 (2008). (Pubitemid 351317439)
15. V. Yu. Gonchar, A. V. Chechkin, E. L. Sorokovoy, V. V. Chechkin, L. I. Grigor'eva, and E. D. Volkov, Plasma Phys. Rep. PPHREM 1063-780X 10.1134/1.1575308 29, 380 (2003); (Pubitemid 36803009)
16. T. Mizuuchi, V. V. Chechkin, K. Ohashi, E. L. Sorokovoy, A. V. Chechkin, V. Yu. Gonchar, K. Takahashi, S. Kobayashi, K. Nagasaki, H. Okada, S. Yamamoto, F. Sano, K. Kondo, N. Nishino, H. Kawazome, H. Shidara, S. Kaneko, Y. Fukagawa, Y. Morita, S. Nakazawa, S. Nishio, S. Tsuboi, and M. Yamada, J. Nucl. Mater. JNUMAM 0022-3115 10.1016/j.jnucmat.2004.10.010 337-339, 332 (2005). (Pubitemid 40259257)
17. R. Jha, P. K. Kaw, D. R. Kulkarni, J. C. Parikh, and (ADITYA Team), Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1541607 10, 699 (2003).
18. P. D. Ditlevsen, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.172 60, 172 (1999).
19. C.-K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, and A. L. Goldberger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1343 70, 1343 (1993).
20. C. L. Nikias and M. Shao, Signal Processing with Alpha-Stable Distributions and Applications (Wiley, New York, 1995).
21. K. Burnecki and A. Weron, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.021130 82, 021130 (2010).
22. R. N. Mantegna and S. E. Stanley, An Introduction to Econophysics (Cambridge University Press, Cambridge, 2000).
23. W. H. DuMouchel, Ann. Statist. ASTSC7 0090-5364 10.1214/aos/1176342516 1, 948 (1973);
24. J. P. Nolan, in Lévy Processes. Theory and Applications, edited by, O. E. Barndorff-Nielsen, T. Mikosch, and, S. I. Resnick, (Birkhäuser, Boston, 2001).
25. J. H. McCulloch, Commun. Statist. Simul. Comput. CSSCDB 0361-0918 10.1080/03610918608812563 15, 1109 (1986).
26. I. A. Koutrouvelis, J. Amer. Statist. Assoc. 75, 918 (1980);
27. I. A. Koutrouvelis, Commun. Statist. Simul. Comput. CSSCDB 0361-0918 10.1080/03610918108812189 10, 17 (1981);
28. S. M. Kogon, D. B. Williams, in A Practical Guide to Heavy Tails, edited by, R. Adler, R. Feldman, and, M. Taqqu, (Birkhäuser, Boston, 1998).
29. B. M. Hill, Ann. Statist. ASTSC7 0090-5364 10.1214/aos/1176343247 3, 1163 (1975).
30. R. Weron, Int. Journ. Mod. Phys. C IJMPEO 0129-1831 10.1142/ S0129183101001614 12, 209 (2001).
31. J. Janczura and A. Wyłomańska, Acta Phys. Polon. B 40, 1341 (2009).
32. S. Borak, W. Haerdle, and R. Weron, Stable Distributions. SFB 649 Discussion Paper 2005-008 (available at [http://sfb649.wiwi.hu-berlin.de]).
33. R. B. D'Agostino and M. A. Stephens, Goodness-of-Fit Techniques (Marcel Dekker, New York, 1986).
34. C. M. Jarque and A. K. Bera, Internat. Statist. Rev. 0306-7734 10.2307/1403192 55, 163 (1987).
35. R. Weron, in Handbook of Computational Statistics: Concepts and Methods, edited by, J. E. Gentle, W. Härdle, and, Y. Mori, (Springer, Berlin, 2004).
36. S. Ross, Simulation (Academic Press, San Diego, 2002).
37. K. Burnecki, J. Janczura, and R. Weron, in Statistical Tools for Finance and Insurance, edited by, P. Cizek, W. Härdle, R. Weron, (Springer, Berlin, 2011).
38. F. Wagner, Plasma Phys. Controlled Fusion PPCFET 0741-3335 10.1088/0741-3335/49/12B/S01 49, B1 (2007). (Pubitemid 350151292)
39. [http://www.iter.org/].
40. V. I. Demidov, S. V. Ratynskaia, and K. Rypdal, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.1505099 73, 3409 (2002). (Pubitemid 35328715)
41. A. A. Beletskii, L. I.Grigor'eva, E. L. Sorokovoy, V. V. Chechkin, Y. L. Sorokovoy, Ye.D. Volkov, P. Ya. Burchenko, A. Ye. Kulaga, S. A. Tsybenko, A. V. Lozin, A. S. Slavnyj, Yu.S. Lavrenovich, N. V. Zamanov, Yu. K. Mironov, and V. S. Romanov, Plasma Phys. Rep. PPHREM 1063-780X 10.1134/S1063780X0910002X 35, 818 (2009).
42. V. V. Chechkin, L. I. Grigor'eva, E. L. Sorokovoy, Ye. L. Sorokovoy, A. S. Slavnyj, Ye. D. Volkov, A. A. Beletskii, P. Ya. Burchenko, S. A. Tsybenko, A. V. Lozin, A. Ye. Kulaga, A. P. Litvinov, S. Masuzaki, and K. Yamazaki, Plasma Phys. Controlled Fusion PPCFET 0741-3335 10.1088/0741-3335/48/5A/S22 48, A241 (2006).
43. J. P. Nolan, in Proceedings of the ASA-IMS Conference on Applications of Heavy Tailed Distributions in Economics, Engineering and Statistics, June 3-5, 1999, Washington, DC, edited by, J. P. Nolan, and, A. Swami, (TSI Press, Albequerque, 1999).
44. B. M. Brown and T. P. Hettmansperger, J. Amer. Statist. Assoc. 91, 1668 (1996).
45. V. Yu. Korolev and N. N. Skvortsova, Stochastic Models of Structural Plasma Turbulence (VSP, Leiden/Boston, 2006).
46. R. O. Dendy and S. C. Chapman, Plasma Phys. Controlled Fusion PPCFET 0741-3335 10.1088/0741-3335/48/12B/S30 48, B313 (2006).
47. N. W. Watkins, D. Credgington, R. Sanchez, S. J. Rosenberg, and S. C. Chapman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.041124 79, 041124 (2009).