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Methods to Distinguish Between Polynomial and Exponential Tails

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  • Joan Del Castillo
  • Jalila Daoudi
  • Richard Lockhart

Abstract

type="main" xml:id="sjos12037-abs-0001"> Two methods to distinguish between polynomial and exponential tails are introduced. The methods are based on the properties of the residual coefficient of variation for the exponential and non-exponential distributions. A graphical method, called a CV-plot, shows departures from exponentiality in the tails. The plot is applied to the daily log-returns of exchange rates of US dollar and Japanese yen. New statistics are introduced for testing the exponentiality of tails using multiple thresholds. They give better control of the significance level than previous tests. The powers of the new tests are compared with those of some others for various sample sizes.

Suggested Citation

  • Joan Del Castillo & Jalila Daoudi & Richard Lockhart, 2014. "Methods to Distinguish Between Polynomial and Exponential Tails," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 382-393, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:382-393
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    File URL: http://hdl.handle.net/10.1111/sjos.12037
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    References listed on IDEAS

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    1. del Castillo, Joan & Daoudi, Jalila, 2009. "Estimation of the generalized Pareto distribution," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 684-688, March.
    2. Gel, Yulia R., 2010. "Test of fit for a Laplace distribution against heavier tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 958-965, April.
    3. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    4. Gel, Yulia R. & Miao, Weiwen & Gastwirth, Joseph L., 2007. "Robust directed tests of normality against heavy-tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2734-2746, February.
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    2. Marek Arendarczyk & Tomasz J. Kozubowski & Anna K. Panorska, 2022. "The Greenwood statistic, stochastic dominance, clustering and heavy tails," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 331-352, March.
    3. Matteo Fusi & Fabio Mazzocchetti & Albert Farres & Leonidas Kosmidis & Ramon Canal & Francisco J. Cazorla & Jaume Abella, 2020. "On the Use of Probabilistic Worst-Case Execution Time Estimation for Parallel Applications in High Performance Systems," Mathematics, MDPI, vol. 8(3), pages 1-21, March.
    4. Albrecher, Hansjörg & García Flores, Brandon, 2022. "Asymptotic analysis of generalized Greenwood statistics for very heavy tails," Statistics & Probability Letters, Elsevier, vol. 185(C).
    5. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.

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