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The Anderson-Darling test of fit for the power law distribution from left censored samples

Author

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  • H. F. Coronel-Brizio

    (Facultad de Fisica e Inteligencia Artificial, Departamento de Inteligencia Artificial, Universidad Veracruzana, Mexico)

  • A. R. Hernandez-Montoya

    (Facultad de Fisica e Inteligencia Artificial, Departamento de Inteligencia Artificial, Universidad Veracruzana, Mexico)

Abstract

Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum likelihood estimators and tables of asymptotic percentage points for the A^2 statistic are given. The technique is illustrated for data from the Dow Jones Industrial Average index, an example of high theoretical and practical importance in Econophysics, Finance, Physics, Biology and, in general, in other related Sciences such as Complexity Sciences.

Suggested Citation

  • H. F. Coronel-Brizio & A. R. Hernandez-Montoya, 2010. "The Anderson-Darling test of fit for the power law distribution from left censored samples," Papers 1004.0417, arXiv.org.
    • Handle: RePEc:arx:papers:1004.0417
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    File URL: http://arxiv.org/pdf/1004.0417
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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    Cited by:

    1. Politi, Mauro & Millot, Nicolas & Chakraborti, Anirban, 2012. "The near-extreme density of intraday log-returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 147-155.
    2. Fujimoto, Shouji & Ishikawa, Atushi & Mizuno, Takayuki & Watanabe, Tsutomu, 2011. "A new method for measuring tail exponents of firm size distributions," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 5, pages 1-20.
    3. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Papers 1106.0039, arXiv.org.
    4. Afsin Sahin, 2023. "Testing Distributions in Banking Sector Loans with Different Computer Programs: An Experimental Analysis for Turkey," Athens Journal of Business & Economics, Athens Institute for Education and Research (ATINER), vol. 9(2), pages 145-158, April.
    5. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Post-Print hal-00827942, HAL.
    6. Yongli Li & Tianchen Wang & Baiqing Sun & Chao Liu, 2022. "Detecting the lead–lag effect in stock markets: definition, patterns, and investment strategies," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-36, December.

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