Geometric theory for Weibull's distribution

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

Volumn 86, Issue 3, 2012, Pages

  Eliazar, Iddo ^a  

^a HOLON INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRIC THEORY; LINEAR SCALING; PHYSICAL SCIENCE; PROBABILISTIC THEORY; RANDOM ENVIRONMENT; RELAXATION REGIMES; SPATIAL GEOMETRY; STRETCHED EXPONENTIAL; WEIBULL;

CONDENSED MATTER PHYSICS; PHYSICS;

WEIBULL DISTRIBUTION;

EID: 84865968686     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.031103     Document Type: Article

References (75)

1. W. Weibull, Ingeniors Vetenskaps Akademiens, Stockholm 151 (1939);
2. W. Weibull, ASME J. Appl. Mech. 18, 293 (1951).
3. E. J. Gumbel, Statistics of Extremes (Dover, Mineola, 2004;
4. originally published by Columbia University Press in 1958).
5. J. Galambos, Asymptotic Theory of Extreme Order Statistics, 2nd ed. (Krieger, Melbourne, FL, 1987).
6. S. Kotz and S. Nadarajah, Extreme Value Distributions (Imperial College Press, London, 2000).
7. J. Beirlant, Y. Goegebeur, J. Segers, and J. Teugels, Statistics of Extremes: Theory and Applications (Wiley, New York, 2004).
8. L. de Haan and Ana Ferreira, Extreme Value Theory: An Introduction (Springer, New York, 2006).
9. R. D. Reiss and M. Thomas, Statistical Analysis of Extreme Values: With Applications to Insurance, Finance, Hydrology and Other Fields (Birkhauser, Basel, 2007).
10. M. Fréchet, Ann. Soc. Polon. Math. Cracovie 6, 93 (1927).
11. R. A. Fisher and L. H. C. Tippett, Proc. Cambridge Phil. Soc. MPCPCO 0305-0041 10.1017/S0305004100015681 24, 180 (1928).
12. B. Gnedenko, Ann. Math. ANMAAH 0003-486X 10.2307/1968974 44, 423 (1943)
13. [Translated and reprinted in: Breakthroughs in Statistics I, edited by S. Kotz and N. L. Johnson (Springer, New York, 1992)], pp. 195-225.
14. D. N. P. Murthy, M. Xie, and R. Jiang, Weibull Models (Wiley, New York, 2003).
15. B. Dodson, The Weibull Analysis Handbook (ASQ Press, Milwaukee, 2006).
16. R. Abernethy, The New Weibull Handbook, 5th ed. (Dr. Robert. Abernethy, 2006).
17. H. Rinne, The Weibull Distribution: A Handbook (CRC Press, Boca Raton, FL, 2008).
18. J. I. McCool, Using the Weibull Distribution: Reliability, Modeling and Inference (Wiley, New York, 2012).
19. J. Laherrere and D. Sornette, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050276 2, 525 (1998).
20. J. C. Phillips, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/59/9/ 003 59, 1133 (1996).
21. C. Gardiner, Handbook of Stochastic Methods (Springer, New York, 2004).
22. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd ed. (North-Holland, Amsterdam, 2007).
23. W. T. Coffey and Yu. P. Kalmykov, Fractals, Diffusions and Relaxation in Disordered Systems (Wiley-Interscience, New York, 2006).
24. R. Kohlrausch, Pogg. Ann. Phys. Chem. 91, 56 (1854);
25. R. Kohlrausch, Pogg. Ann. Phys. Chem. 91, 179 (1854).
26. F. Kohlrausch, Pogg. Ann. Phys. Chem. 119, 337 (1863).
27. A. Werner, Ann. Phys. ANPYA2 0003-3804 10.1002/andp.19073291111 24, 164 (1907).
28. E. W. Montroll, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1724118 14, 202 (1946).
29. T. Forster, Z. Natur. 4, 321 (1949).
30. B. Y. Sveshnikov and V. I. Shirokov, Opt. Spec. 12, 576 (1962).
31. M. Inokuti and F. Hirayama, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1697063 43, 1978 (1965).
32. G. Williams and D. C. Watts, Trans. Faraday Soc. TFSOA4 0014-7672 10.1039/tf9706600080 66, 80 (1970).
33. R. V. Chamberlin, G. Mozurkewich, and R. Orbach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.867 52, 867 (1984).
34. I. A. Campbell, J. M. Flesselles, R. Jullien, and R. Botet, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.37.3825 37, 3825 (1988).
35. G. Kriza and G. Mihaly, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.2529 56, 2529 (1986).
36. J. Kakalios, R. A. Street, and W. B. Jackson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.1037 59, 1037 (1987).
37. V. Degiorgio, T. Bellini, R. Piazza, F. Mantegazza, and R. E. Goldstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1043 64, 1043 (1990).
38. E. Rabani, J. D. Gezelter, and B. J. Berne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3649 82, 3649 (1999).
39. I. Eliazar and J. Klafter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.021122 82, 021122 (2010).
40. I. Eliazar, "Statistical universality and the method of Poissonian ran-domizations", European Phys. J. ST (in press, 2013).
41. A. Blumen, Nuovo Cimento Soc. Ital. Fis. B NCIBAW 0369-3554 10.1007/BF02721411 63, 50 (1981).
42. R. G. Palmer, D. L. Stein, E. Abrahams, and P. W. Anderson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.958 53, 958 (1984).
43. M. F. Shlesinger and E. W. Montroll, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.81.4.1280 81, 1280 (1984).
44. K. Weron, J. Phys. Cond. Matt. JCOMEL 0953-8984 10.1088/0953-8984/3/46/ 016 3, 9151 (1991).
45. P. Jund, R. Jullien, and I. Campbell, Phys. Rev. E 1539-3755 10.1103/PhysRevE.63.036131 63, 036131 (2001).
46. R. Reigada, A. Sarmiento, and K. Lindenberg, Physica A PHYADX 0378-4371 10.1016/S0378-4371(01)00573-8 305, 467 (2002). (Pubitemid 34232282)
47. M. Moreau, G. Oshanin, O. Benichou, and M. Coppey, Physica A PHYADX 0378-4371 10.1016/S0378-4371(03)00458-8 327, 99 (2003).
48. N. Lemke and I. A. Campbell, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.041126 84, 041126 (2011).
49. I. Eliazar and O. Benichou, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/45/1/015003 45, 015003 (2012).
50. I. Eliazar and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2011.11.001 511, 143 (2012).
51. J. Klafter and M. F. Shlesinger, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.83.4.848 83, 848 (1986).
52. S. B. Yuste, J. J. Ruiz-Lorenzo, and K. Lindenberg, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.046119 74, 046119 (2006). (Pubitemid 44684169)
53. S. B. Yuste and K. Lindenberg, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.051114 76, 051114 (2007). (Pubitemid 350126063)
54. I. Eliazar, T. Koren, and J. Klafter, J. Phys. C: Cond. Matt. JCOMEL 0953-8984 10.1088/0953-8984/19/6/065140 19, 065140 (2007); (Pubitemid 46478517)
55. I. Eliazar, T. Koren, and J. Klafter, J. Phys. Chem. B JPCBFK 1520-6106 10.1021/jp075113k 112, 5905 (2008).
56. S. B. Yuste, G. Oshanin, K. Lindenberg, O. Benichou, and J. Klafter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.021105 78, 021105 (2008).
57. I. Eliazar and J. Klafter, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/44/22/222001 44, 222001 (2011).
58. N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation (Cambridge University Press, Cambridge, UK, 1987).
59. S. M. Ross, Applied Probability Models with Optimization Applications (Holden-Day, San Francisco, CA 1970).
60. H. C. Tijms, Stochastic Models: An Algorithmic Approach (Wiley, New York, 1995).
61. E. Barlow and F. Proschan, Mathematical Theory of Reliability (SIAM, Providence, RI, 1996).
62. J. F. C. Kingman, Poisson Processes (Oxford University Press, Oxford, UK, 1993).
63. D. R. Cox and V. Isham, Point Processes (CRC, Boca Raton, FL, 2000).
64. R. L. Streit, Poisson Point Processes (Springer, New York, 2010).
65. P. Embrechts, C. Kluppelberg, and T. Mikosch, Modelling Extremal Events for Insurance and Finance (Springer, New York, 1997).
66. R. W. Wolff, Stochastic Modeling and the Theory of Queues (Prentice-Hall, London, 1989).
67. S. B. Lowen and M. C. Teich, Fractal-based Point Processes (Wiley, New York, 2005).
68. H. S. Heaps, Information Retrieval: Computational and Theoretical Aspects (Academic Press, Boston, 1978).
69. R. Baeza-Yates and G. Navarro, J. Am. Soc. Inform. Sci. 0002-8231 10.1002/(SICI)1097-4571(2000)51:1<69::AID-ASI10>3.0.CO;2-C 51, 69 (2000). (Pubitemid 30526376)
70. D. C. van Leijenhorst and Th. P. van der Weide, Inform. Sci. ISIJBC 0020-0255 10.1016/j.ins.2004.03.006 170, 263 (2005). (Pubitemid 40183409)
71. C. Cattutoa, Proc. Natl. Acad. Sci. USA 106, 10511 (2009).
72. M. A. Serrano, A. Flammini and F. Menczer, PLoS ONE 1932-6203 10.1371/journal.pone.0005372 4, e5372 (2009).
73. L. Lu, Z. K. Zhang and T. Zhou, PLoS ONE 1932-6203 10.1371/journal.pone. 0014139 5, e14139 (2010).
74. H. Hu, D. Han, and X. Wang, Physica A PHYADX 0378-4371 10.1016/j.physa.2009.11.007 389, 1065 (2010).
75. I. Eliazar, Physica A PHYADX 0378-4371 10.1016/j.physa.2011.05.003 390, 3189 (2011).