Power-law distributions: Beyond Paretian fractality

Risk and Decision Analysis

Volumn 1, Issue 3, 2009, Pages 155-170

  Eliazar, Iddo ^a   Klafter, Joseph ^b,c  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Fr chet; Paretian fractality; Poisson processes; Poissonian fractality and renormalization; renormalization; Weibull and L vy stable distributions

Indexed keywords

EID: 77954529514     PISSN: 15697371     EISSN: 18759173     Source Type: Journal    
DOI: 10.3233/RDA-2009-0014     Document Type: Article

References (25)

1. B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, NY, 1982.
2. J. Feder, Fractals, Plenum Press, New York, NY, 1988.
3. H.O. Peitgen, H. Jurgens and D. Saupe, Chaos and Fractals, Springer, New York, NY, 1992.
4. M.F. Barnsley, Fractals Everywhere, 2nd edn, Academic Press, Boston, MA, 1993.
5. V. Pareto, Cours d'économie politique, Droz, Geneva, 1896.
6. M.F. Shlesinger, G.M. Zaslavsky and J. Klafter, Nature 363 (1993), 31.
7. P. Bak, How Nature Works, Copernicus, New York, NY, 1996.
8. B. Dubrulle, F. Garner and D. Sornette (eds), Scale Invariance and Beyond, EDP Sciences and Springer, Berlin, 1997.
9. J. Klafter and I.M. Sokolov, Physics World 18 (2005), 29.
10. M.E.J. Newman, Contemp. Phys. 46 (2005), 323.
11. I. Eliazar and J. Klafter, Physica A 383 (2007), 171.
12. D. Sornette, Self-organized criticality in plate tectonics, in: Proceedings of the NATO ASI Spontaneous Formation of Space-Time Structures and Criticality, T. Riste and D. Sherrington, eds, Kluwer, Boston, MA, 1991, pp. 57-106.
13. I. Eliazar and J. Klafter, Phys. Rev. E 77 (2008), 061125.
14. W. Feller, An Introduction to Probability Theory and Its Applications, 3rd edn, Vol. I, Wiley, New York, NY, 1968.
15. E. Barlow and F. Proschan, Mathematical Theory of Reliability, Classics in Applied Mathematics 17, reprint edition, Society for Industrial&Applied Mathematics, SIAM, Philadelphia, PA, 1996.
16. H.C. Tijms, Stochastic Models: An Algorithmic Approach, Wiley, New York, NY, 1995.
17. S.M. Ross, Introduction to Probability Models, 8th edn, Academic Press, Boston, MA, 2002.
18. D.V. Widder, The Laplace Transform, Princeton University Press, Princeton, NJ, 1946.
19. B. Gnedenko, Ann. Math. 44 (1943), 423 (translated and reprinted in Breakthroughs in Statistics I, S. Kotz and N.L. Johnson, eds, Springer, New York, NY, 1992, pp. 195-225).
20. E.J. Gumbel, Statistics of Extremes, Columbia University Press, New York, NY, 1958.
21. J. Galambos, Asymptotic Theory of Extreme Order Statistics, 2nd edn, Krieger, New York, NY, 1987.
22. P. Lévy, Théorie de l'addition des variables Aléatoires, Gauthier-Villars, Paris, 1954.
23. B.V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, London, 1954.
24. I.A. Ibragimov and Yu.V. Linnik, Independent and Stationary Sequences of Random Variables, Walterss-Noordhoff, Groningen, 1971.
25. J.F.C. Kingman, Poisson Processes, Oxford University Press, Oxford, 1993.