Diversity of Poissonian populations

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

Volumn 81, Issue 1, 2010, Pages

  Eliazar, Iddo I ^a   Sokolov, Igor M ^b  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CUT-OFF; EXTREME-VALUE THEORY; KEY ISSUES; PARTICIPATION RATIOS; POISSON PROCESS; POISSONIAN; PROBABILITY THEORY; RANDOM FRACTALS; REAL LINE; SCIENCE AND ENGINEERING; SHANNON'S ENTROPY; SIMPSON'S INDEX; STATISTICAL MODELING; STATISTICAL PHYSICS;

MEASUREMENT THEORY; POISSON DISTRIBUTION; PROBABILITY DENSITY FUNCTION;

POPULATION STATISTICS;

EID: 75349114027     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.011122     Document Type: Article

References (31)

1. J. F. C. Kingman, Poisson Processes (Oxford University Press, Oxford, 1993).
2. P. Lévy, Théorie de l'Addition des Variables Aleatoires (Gauthier-Villars, Paris, 1954).
3. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, London, 1954).
4. I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables (Walterss-Noordhoff, Groningen, The Netherlands, 1971).
5. B. Gnedenko, Ann. Math. 44, 423 (1943) 10.2307/1968974
6. Translated and reprinted in Breakthroughs in Statistics I, edited by, S. Kotz, and, N. L. Johnson, (Springer, New York, 1992), pp. 195-225.
7. E. J. Gumbel, Statistics of Extremes (Columbia University Press, New York, 1958).
8. J. Galambos, Asymptotic Theory of Extreme Order Statistics, 2nd ed. (Krieger, New York, 1987).
9. I. Eliazar and J. Klafter, Proc. Natl. Acad. Sci. U.S.A. 102, 13779 (2005). 10.1073/pnas.0506816102
10. I. Eliazar and J. Klafter, Phys. Rev. E 75, 031108 (2007). 10.1103/PhysRevE.75.031108
11. I. Eliazar and J. Klafter, Physica A 383, 171 (2007). 10.1016/j.physa.2007.04.044
12. I. Eliazar, Physica A 386, 318 (2007). 10.1016/j.physa.2007.08.003
13. I. Eliazar and J. Klafter, Phys. Rev. E 79, 011103 (2009). 10.1103/PhysRevE.79.011103
14. I. Eliazar and J. Klafter, Proc. Natl. Acad. Sci. U.S.A. 106, 12251 (2009). 10.1073/pnas.0900299106
15. I. Eliazar and J. Klafter, Phys. Rev. Lett. 103, 040602 (2009). 10.1103/PhysRevLett.103.040602
16. E. H. Simpson, Nature (London) 163, 688 (1949). 10.1038/163688a0
17. R. G. Bell, P. Dean, and D. C. Hibbins-Butler, J. Phys. C 3, 2111 (1970) 10.1088/0022-3719/3/10/013
18. R. J. Bell and P. Dean, Philos. Mag. 25, 1381 (1972). 10.1080/14786437208223861
19. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1949).
20. C. Gini, Econ. J. 31, 124 (1921). 10.2307/2223319
21. E. T. Jaynes, Phys. Rev. 106, 620 (1957). 10.1103/PhysRev.106.620
22. R. G. Abraham, S. van den Bergh, and P. Nair, Astrophys. J. 588, 218 (2003). 10.1086/373919
23. P. P. Graczyk, J. Med. Chem. 50, 5773 (2007). 10.1021/jm070562u
24. L. Wittebolle, Nature (London) 458, 623 (2009) 10.1038/nature07840
25. S. Naeem, Nature (London) 458, 579 (2009). 10.1038/458579a
26. P. Embrechts, C. Kluppelberg, and T. Mikosch, Modeling Extremal Events for Insurance and Finance (Springer, New York, 1997).
27. M. Thomas and R. D. Reiss, Statistical Analysis of Extreme Values (Birkhauser, Boston, 2001).
28. R. W. Wolff, Stochastic Modeling and the Theory of Queues (Prentice-Hall, London, 1989).
29. B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993). 10.1088/0034-4885/56/12/001
30. A. Rényi, On measures of entropy and information, in Proceeding of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1960 (University of California Press, Berkeley, 1961), Vol. 1, p. 547.
31. N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation (Cambridge University Press, Cambridge, 1987).