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On tail dependence for Grubbs’ copula-function

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Abstract

We consider Grubbs’ statistics for a normal sample. Those statistics are the standardized maximum and standardized minimum. We investigate the distribution properties of Grubbs’ statistics and construct a new copula-function by an inversion method from the joint distribution of Grubbs’ statistics. We also describe properties of the constructed Grubbs’ copula-function. It is proved that this copula is symmetric. We give examples of plots of the simulated values from Grubbs’ copula. It is found that Grubbs’ copula-function allows to describe negative dependencies between random variables. It is proved that forGrubbs’ copula-function coefficients of the upper-left and lower-right tail dependencies are equal each other. We find the formula for calculation of these coefficients and execute model calculations of tail dependencies coefficients for Grubbs’ copula.

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References

  1. Fantazzini, D. “Analysis of Multidimensional Probability Distributions with Copula Functions. I”, Applied Econometrics 22, No. 2, 98–134 (2011) [in Russian].

    Google Scholar 

  2. Grubbs, F. “Sample Criteria for Testing Outlying Observations”, Ann. Math. Statist. 21, No. 1, 27–58 (1950).

    Article  MATH  MathSciNet  Google Scholar 

  3. Barnett, V., Lewis, T. Outliers in Statistical Data (John Wiley & Sons, Chichester, 1984).

    MATH  Google Scholar 

  4. Zhang, J., Keming, Y. “The Null Distribution of the Likelihood-Ratio Test for One or Two Outliers in a Normal Sample”, AnOfficial J. of the Spanish Soc. of Statistics and Operat. Research 15, No. 1, 141–150 (2006).

    MATH  Google Scholar 

  5. Shiryaeva, L. K. “On Null and Alternative Distribution of Statistic of Two-Side Discordancy Test for an Extreme Outlier”, RussianMathematics (Iz. VUZ) 58, No. 10, 52–66 (2014).

    MATH  Google Scholar 

  6. Nelsen R.B. An Introduction to Copulas. Lecture Notes in Statistics (Springer-Verlag, New York, 2006).

    Google Scholar 

  7. Jahnke, E., Emde, F., Lösch, F. Special Functions (Nauka, Moscow, 1977) [Russian translation].

    Google Scholar 

  8. Fantazzini, D. “Analysis of Multidimensional Probability Distributions with Copula Functions. II”, Applied Econometrics 23, No. 3, 98–132 (2011) [in Russian].

    Google Scholar 

  9. Ammann, M., Suss, S. “Asymmetric Dependence Patterns in Financial Time Series”, The European J. Finance 15, No. 7–8, 703–719 (2009).

    Article  Google Scholar 

  10. Mikeladze, Sh. E. Numerical Methods of Mathematical Analysis (GITTL, Moscow, 1953) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Samara State Economic University, ul. Sovetskoi Armii 141, Samara, 443090, Russia

    L. K. Shiryaeva

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  1. L. K. Shiryaeva
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Correspondence to L. K. Shiryaeva.

Additional information

Original Russian Text © L.K. Shiryaeva, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 12, pp. 66–83.

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Shiryaeva, L.K. On tail dependence for Grubbs’ copula-function. Russ Math. 59, 56–72 (2015). https://doi.org/10.3103/S1066369X15120063

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