메뉴 건너뛰기




Volumn 51, Issue 4, 2009, Pages 661-703

Power-law distributions in empirical data

Author keywords

Heavy tailed distributions; Likelihood ratio test; Maximum likelihood; Model selection; Pareto; Power law distributions; Zipf

Indexed keywords

HEAVY-TAILED DISTRIBUTION; LIKELIHOOD RATIO TEST; LIKELIHOOD RATIO TESTS; MODEL SELECTION; POWER LAW DISTRIBUTION;

EID: 65549085067     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/070710111     Document Type: Review
Times cited : (7405)

References (69)
  • 1
    • 0141922822 scopus 로고    scopus 로고
    • A functional approach to external graph algorithms
    • J. ABELLO, A. L. BUCHSBAUM, AND J. WESTBROOK, A functional approach to external graph algorithms, Algorithmica, 32 (2002), pp. 437-458.
    • (2002) Algorithmica , vol.32 , pp. 437-458
    • Abello, J.1    Buchsbaum, A.L.2    Westbrook, J.3
  • 2
    • 68549135094 scopus 로고    scopus 로고
    • On the bias of traceroute sampling: Or, power-law degree distributions in regular graphs
    • article 21
    • D. ACHLIOPTAS, A. CLAUSET, D. KEMPE, AND C. MOORE, On the bias of traceroute sampling: or, power-law degree distributions in regular graphs, J. ACM, 56 (4) (2009), article 21.
    • (2009) J. ACM , vol.56 , pp. 4
    • Achlioptas, D.1    Clauset, A.2    Kempe, D.3    Moore, C.4
  • 6
    • 0004231080 scopus 로고
    • International Cooperative Publishing House Fairland, MD
    • B. C. ARNOLD, Pareto Distributions, International Cooperative Publishing House, Fairland, MD, 1983.
    • (1983) Pareto Distributions
    • Arnold, B.C.1
  • 8
    • 34547890729 scopus 로고    scopus 로고
    • Parameter estimation for power-law tail distributions by maximum likelihood methods
    • H. BAUKE, Parameter estimation for power-law tail distributions by maximum likelihood methods, Eur. Phys. J. B, 58 (2007), pp. 167-173.
    • (2007) Eur. Phys. J. B , vol.58 , pp. 167-173
    • Bauke, H.1
  • 13
    • 0003665885 scopus 로고
    • R. B. D'AGOSTINO AND M. A. STEPHENS, EDS., Marcel Dekker, New York
    • R. B. D'AGOSTINO AND M. A. STEPHENS, EDS., Goodness-of-Fit Techniques, Marcel Dekker, New York, 1986.
    • (1986) Goodness-of-Fit Techniques
  • 18
    • 0001735517 scopus 로고
    • On the mathematical foundations of theoretical statistics
    • R. A. FISHER, On the mathematical foundations of theoretical statistics, Philos. Trans. Roy. Soc. London Ser. A, 222 (1922), pp. 309-368.
    • (1922) Philos. Trans. Roy. Soc. London Ser. A , vol.222 , pp. 309-368
    • Fisher, R.A.1
  • 19
    • 10044260009 scopus 로고    scopus 로고
    • Problems with fitting to the power-law distribution
    • M. L. GOLDSTEIN, S. A. MORRIS, AND G. G. YEN, Problems with fitting to the power-law distribution, Eur. Phys. J. B, 41 (2004), pp. 255-258.
    • (2004) Eur. Phys. J. B , vol.41 , pp. 255-258
    • Goldstein, M.L.1    Morris, S.A.2    Yen, G.G.3
  • 22
    • 0002407801 scopus 로고
    • On some simple estimates of an exponent of regular variation
    • P. HALL, On some simple estimates of an exponent of regular variation, J. Roy. Statist. Soc. Ser. B, 44 (1982), pp. 37-42
    • (1982) J. Roy. Statist. Soc. Ser. B , vol.44 , pp. 37-42
    • Hall, P.1
  • 23
    • 2442551914 scopus 로고    scopus 로고
    • Likelihood-based inference for stochastic models of sexual network formation
    • M. S. HANDCOCK AND J. H. JONES, Likelihood-based inference for stochastic models of sexual network formation, Theoret. Population Biol., 65 (2004), pp. 413-422.
    • (2004) Theoret. Population Biol. , vol.65 , pp. 413-422
    • Handcock, M.S.1    Jones, J.H.2
  • 24
    • 0001263124 scopus 로고
    • A simple general approach to inference about the tail of a distribution
    • B. M. HILL, A simple general approach to inference about the tail of a distribution, Ann. Statist., 3 (1975), pp. 1163-1174.
    • (1975) Ann. Statist. , vol.3 , pp. 1163-1174
    • Hill, B.M.1
  • 26
    • 34548425218 scopus 로고    scopus 로고
    • Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks
    • M. HUSS AND P. HOLME, Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks, IET Systems Biol., 1 (2007), pp. 280-285.
    • (2007) IET Systems Biol. , vol.1 , pp. 280-285
    • Huss, M.1    Holme, P.2
  • 28
    • 0033974688 scopus 로고    scopus 로고
    • Toward a protein-protein interaction map of the budding yeast: A comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins
    • T. ITO, K. TASHIRO, S. MUTA, R. OZAWA, T. CHIBA, M. NISHIZAWA, K. YAMAMOTO, S. KUHARA, AND Y. SAKAKI, Toward a protein-protein interaction map of the budding yeast: A comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 1143-1147.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 1143-1147
    • Ito, T.1    Tashiro, K.2    Muta, S.3    Ozawa, R.4    Chiba, T.5    Nishizawa, M.6    Yamamoto, K.7    Kuhara, S.8    Sakaki, Y.9
  • 29
    • 33846432342 scopus 로고
    • Some tests of significance treated by the theory of probability
    • H. JEFFREYS, Some tests of significance treated by the theory of probability, Proc. Cambridge Philos. Soc., 31 (1935), pp. 203-222.
    • (1935) Proc. Cambridge Philos. Soc. , vol.31 , pp. 203-222
    • Jeffreys, H.1
  • 32
    • 0034310714 scopus 로고    scopus 로고
    • Connectivity of growing random networks
    • P. L. KRAPIVSKY, S. REDNER, AND F. LEYVRAZ, Connectivity of growing random networks, Phys. Rev. Lett., 85 (2000), pp. 4629-4632.
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 4629-4632
    • Krapivsky, P.L.1    Redner, S.2    Leyvraz, F.3
  • 33
    • 0000562848 scopus 로고    scopus 로고
    • The qq-estimator and heavy tails
    • M. KRATZ AND S. I. RESNICK, The qq-estimator and heavy tails, Stoch. Models, 12 (1996), pp. 699-724.
    • (1996) Stoch. Models , vol.12 , pp. 699-724
    • Kratz, M.1    Resnick, S.I.2
  • 35
    • 24144465546 scopus 로고    scopus 로고
    • Empirical distributions of log-returns: Between the stretched exponential and the power law?
    • Y. MALEVERGNE, V. F. PISARENKO, AND D. SORNETTE, Empirical distributions of log-returns: Between the stretched exponential and the power law?, Quant. Finance, 5 (2005), pp. 379-401.
    • (2005) Quant. Finance , vol.5 , pp. 379-401
    • Malevergne, Y.1    Pisarenko, V.F.2    Sornette, D.3
  • 36
    • 0034273073 scopus 로고    scopus 로고
    • Nonparametric estimation of long-tailed density functions and its application to the analysis of World Wide Web traffic
    • N. M. MARKOVITCH AND U. R. KRIEGER, Nonparametric estimation of long-tailed density functions and its application to the analysis of World Wide Web traffic, Performance Eval., 42 (2000), pp. 205-222.
    • (2000) Performance Eval. , vol.42 , pp. 205-222
    • Markovitch, N.M.1    Krieger, U.R.2
  • 37
    • 0000782528 scopus 로고
    • Laws of large numbers for sums of extreme values
    • D. MASON, Laws of large numbers for sums of extreme values, Ann. Probab., 10 (1982), pp. 754-764.
    • (1982) Ann. Probab. , vol.10 , pp. 754-764
    • Mason, D.1
  • 39
    • 57249083246 scopus 로고    scopus 로고
    • Frequentist statistics as a theory of inductive inference
    • J. Rojo, ed., Institute of Mathematical Statistics, Bethesda, MD
    • D. G. MAYO AND D. R. Cox, Frequentist statistics as a theory of inductive inference, in Optimally: The Second Erich L. Lehmann Symposium, J. Rojo, ed., Institute of Mathematical Statistics, Bethesda, MD, 2006, pp. 77-97.
    • (2006) Optimality: The Second Erich L. Lehmann Symposium , pp. 77-97
    • Mayo, D.G.1    Cox, D.R.2
  • 40
    • 79960601554 scopus 로고    scopus 로고
    • A brief history of generative models for power law and lognormal distributions
    • M. MITZENMACHER, A brief history of generative models for power law and lognormal distributions, Internet Math., 1 (2004), pp. 226-251.
    • (2004) Internet Math. , vol.1 , pp. 226-251
    • Mitzenmacher, M.1
  • 41
    • 84924110183 scopus 로고    scopus 로고
    • The future of power law research
    • M. MITZENMACHER, The future of power law research, Internet Math., 2 (2006), pp. 525-534.
    • (2006) Internet Math. , vol.2 , pp. 525-534
    • Mitzenmacher, M.1
  • 42
    • 33749436576 scopus 로고
    • On measures of location and dispersion and tests of hypotheses in a Pareto population
    • A. N. M. MUNIRUZZAMAN, On measures of location and dispersion and tests of hypotheses in a Pareto population, Bull. Calcutta Statist. Assoc, 7 (1957), pp. 115-123.
    • (1957) Bull. Calcutta Statist. Assoc. , vol.7 , pp. 115-123
    • Muniruzzaman, A.N.M.1
  • 43
    • 24744469980 scopus 로고    scopus 로고
    • Power laws, Pareto distributions and Zipf's law
    • M. E. J. NEWMAN, Power laws, Pareto distributions and Zipf's law, Contemp. Phy., 46 (2005), pp. 323-351.
    • (2005) Contemp. Phy. , vol.46 , pp. 323-351
    • Newman, M.E.J.1
  • 44
    • 37649029105 scopus 로고    scopus 로고
    • Email networks and the spread of computer viruses
    • article 035101
    • M. E. J. NEWMAN, S. FORREST, AND J. BALTHROP, Email networks and the spread of computer viruses, Phys. Rev. E, 66 (2002), article 035101.
    • (2002) Phys. Rev. E , vol.66
    • Newman, M.E.J.1    Forrest, S.2    Balthrop, J.3
  • 47
    • 0031622508 scopus 로고    scopus 로고
    • How popular is your paper? An empirical study of the citation distribution
    • S. REDNER, HOW popular is your paper? An empirical study of the citation distribution, Eur. Phys. J. B, 4 (1998), pp. 131-134.
    • (1998) Eur. Phys. J. B , vol.4 , pp. 131-134
    • Redner, S.1
  • 49
    • 0001389839 scopus 로고    scopus 로고
    • Fractality and self-organized criticality of wars
    • D. C. ROBERTS AND D. L. TURCOTTE, Fractality and self-organized criticality of wars, Fractals, 6 (1998), pp. 351-357.
    • (1998) Fractals , vol.6 , pp. 351-357
    • Roberts, D.C.1    Turcotte, D.L.2
  • 50
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • G. SCHWARZ, Estimating the dimension of a model, Ann. Statist., 6 (1978), pp. 461-464.
    • (1978) Ann. Statist. , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 51
    • 0011397517 scopus 로고
    • The maximum likelihood fitting of the discrete Pareto law
    • H. L. SEAL, The maximum likelihood fitting of the discrete Pareto law, J. Inst. Actuaries, 78 (1952), pp. 115-121.
    • (1952) J. Inst. Actuaries , vol.78 , pp. 115-121
    • Seal, H.L.1
  • 56
    • 0037432528 scopus 로고    scopus 로고
    • How reliable are experimental protein-protein interaction data
    • E. SPRINZAK, S. SATTATH, AND H. MARGALIT, HOW reliable are experimental protein-protein interaction data, J. Molecular Biol., 327 (2003), pp. 919-923.
    • (2003) J. Molecular Biol. , vol.327 , pp. 919-923
    • Sprinzak, E.1    Sattath, S.2    Margalit, H.3
  • 58
    • 0000629975 scopus 로고
    • Cross-validatory choice and assessment of statistical predictions
    • M. STONE, Cross-validatory choice and assessment of statistical predictions, J. Roy. Statist. Soc. Ser. B, 36 (1974), pp. 111-133.
    • (1974) J. Roy. Statist. Soc. Ser. B , vol.36 , pp. 111-133
    • Stone, M.1
  • 59
    • 33750468858 scopus 로고    scopus 로고
    • Comment on Barabdsi
    • Preprint, 2005; available at
    • D. B. STOUFFER, R. D. MALMGREN, AND L. A. N. AMARAL, Comment on Barabdsi, Nature, 435, 207 (2005), Preprint, 2005; available at http://arxiv.org/abs/ physics/0510216
    • (2005) Nature , vol.435 , pp. 207
    • Stouffer, D.B.1    Malmgren, R.D.2    Amaral, L.A.N.3
  • 60
    • 0001560641 scopus 로고
    • Fully exponential laplace approximations to expectations and variances of nonpositive functions
    • L. TIERNEY, R. E. KASS, AND J. B. KADANE, Fully exponential Laplace approximations to expectations and variances of nonpositive functions, J. Amer. Statist. Assoc, 84 (1989), pp. 710-716.
    • (1989) J. Amer. Statist. Assoc. , vol.84 , pp. 710-716
    • Tierney, L.1    Kass, R.E.2    Kadane, J.B.3
  • 61
    • 0001223225 scopus 로고    scopus 로고
    • Are citations of scientific papers a case of nonextensivity?
    • C. TSALLIS AND M. P. DE ALBUQUERQUE, Are citations of scientific papers a case of nonextensivity?, Eur. Phys. J. B, 13 (1999), pp. 777-780.
    • (1999) Eur. Phys. J. B , vol.13 , pp. 777-780
    • Tsallis, C.1    De Albuquerque, M.P.2
  • 62
    • 0000646447 scopus 로고
    • Likelihood ratio tests for model selection and non-nested hypotheses
    • Q. H. VUONG, Likelihood ratio tests for model selection and non-nested hypotheses, Economet-rica, 57 (1989), pp. 307-333.
    • (1989) Econometrica , vol.57 , pp. 307-333
    • Vuong, Q.H.1
  • 64
    • 34447342786 scopus 로고    scopus 로고
    • Frequentist bayes is objective
    • L. WASSERMAN, Frequentist Bayes is objective, Bayesian Anal., 1 (2006), pp. 451-456.
    • (2006) Bayesian Anal. , vol.1 , pp. 451-456
    • Wasserman, L.1
  • 66
    • 3242776992 scopus 로고    scopus 로고
    • A Bayesian approach to solar flare prediction
    • M. S. WHEATLAND, A Bayesian approach to solar flare prediction, Astrophys. J., 609 (2004), pp. 1134-1139.
    • (2004) Astrophys. J. , vol.609 , pp. 1134-1139
    • Wheatland, M.S.1
  • 67
    • 0001972601 scopus 로고
    • The large sample distribution of the likelihood ratio for testing composite hypotheses
    • S. S. WILKS, The large sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Statist., 9 (1938), pp. 60-62.
    • (1938) Ann. Math. Statist. , vol.9 , pp. 60-62
    • Wilks, S.S.1
  • 68
    • 0000690179 scopus 로고    scopus 로고
    • Where mathematics meets the internet
    • W. WILLINGER AND V. PAXSON, Where mathematics meets the Internet, Notices Amer. Math. Soc., 45 (1998), pp. 961-970.
    • (1998) Notices Amer. Math. Soc. , vol.45 , pp. 961-970
    • Willinger, W.1    Paxson, V.2
  • 69
    • 1842580761 scopus 로고    scopus 로고
    • Functional and topological characterization of protein interaction networks
    • S.-H. YOOK, Z. N. OLTVAI, AND A.-L. BARABÁSI, Functional and topological characterization of protein interaction networks, Proteomics, 4 (2004), pp. 928-942.
    • (2004) Proteomics , vol.4 , pp. 928-942
    • Yook, S.-H.1    Oltvai, Z.N.2    Barabási, A.-L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.