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On the q-type distributions

Author

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  • Nadarajah, Saralees
  • Kotz, Samuel

Abstract

Various q-type distributions have appeared in the physics literature in the recent years, see e.g. L.C. Malacarne, R.S. Mendes, E. K. Lenzi, q-exponential distribution in urban agglomeration, Phys. Rev. E 65, (2002) 017106. S.M.D. Queiros, On a possible dynamical scenario leading to a generalised Gamma distribution, in xxx.lanl.gov-physics/0411111. U.M.S. Costa, V.N. Freire, L.C. Malacarne, R.S. Mendes, S. Picoli Jr., E.A. de Vasconcelos, E.F. da Silva Jr., An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution, Physica A 361, (2006) 215. S. Picoli, Jr., R.S. Mendes, L.C. Malacarne, q-exponential, Weibull, and q-Weibull distributions: an empirical analysis, Physica A 324 (2003) 678–688. A.M.C. de Souza, C. Tsallis, Student's t- and r- distributions: unified derivation from an entropic variational principle, Physica A 236 (1997) 52–57. It is pointed out in the paper that many of these are the same as or particular cases of what has been known in the statistics literature. Several of these statistical distributions are discussed and references provided. We feel that this paper could be of assistance for modeling problems of the type considered by L.C. Malacarne, R.S. Mendes, E. K. Lenzi, q-exponential distribution in urban agglomeration, Phys. Rev. E 65, (2002) 017106. S.M.D. Queiros, On a possible dynamical scenario leading to a generalised Gamma distribution, in xxx.lanl.gov-physics/0411111. U.M.S. Costa, V.N. Freire, L.C. Malacarne, R.S. Mendes, S. Picoli Jr., E.A. de Vasconcelos, E.F. da Silva Jr., An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution, Physica A 361, (2006) 215. S. Picoli, Jr., R.S. Mendes, L.C. Malacarne, q-exponential, Weibull, and q-Weibull distributions: an empirical analysis, Physica A 324 (2003) 678–688. A.M.C. de Souza, C. Tsallis, Student's t- and r- distributions: unified derivation from an entropic variational principle, Physica A 236 (1997) 52–57 and others.

Suggested Citation

  • Nadarajah, Saralees & Kotz, Samuel, 2007. "On the q-type distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 465-468.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:2:p:465-468
    DOI: 10.1016/j.physa.2006.11.054
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    References listed on IDEAS

    as
    1. Costa, U.M.S. & Freire, V.N. & Malacarne, L.C. & Mendes, R.S. & Picoli Jr., S. & de Vasconcelos, E.A. & da Silva Jr., E.F., 2006. "An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 209-215.
    2. Picoli, S. & Mendes, R.S. & Malacarne, L.C., 2003. "q-exponential, Weibull, and q-Weibull distributions: an empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 678-688.
    3. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
    4. de Souza, AndréM.C. & Tsallis, Constantino, 1997. "Student's t- and r-distributions: Unified derivation from an entropic variational principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(1), pages 52-57.
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    Cited by:

    1. Xiang Jia & Saralees Nadarajah & Bo Guo, 2020. "Inference on q-Weibull parameters," Statistical Papers, Springer, vol. 61(2), pages 575-593, April.
    2. Mark Levene & Aleksejus Kononovicius, 2018. "Empirical Survival Jensen-Shannon Divergence as a Goodness-of-Fit Measure for Maximum Likelihood Estimation and Curve Fitting," Papers 1809.11052, arXiv.org, revised Jun 2019.
    3. Zhang, Ting & Gu, Gao-Feng & Xu, Hai-Chuan & Xiong, Xiong & Chen, Wei & Zhou, Wei-Xing, 2017. "Power-law tails in the distribution of order imbalance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 201-208.
    4. Ewin Sánchez, 2023. "Q-Weibull distribution to explain the PM2.5 air pollution concentration in Santiago de Chile," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-8, August.
    5. Gu, Gao-Feng & Ren, Fei & Ni, Xiao-Hui & Chen, Wei & Zhou, Wei-Xing, 2010. "Empirical regularities of opening call auction in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 278-286.

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