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Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 12, Pages 66–83 (Mi ivm9063)  

This article is cited in 3 scientific papers (total in 3 papers)

On tail dependence for Grubbs' copula-function

L. K. Shiryaeva

Chair of Mathematical Statistics and Econometrics, Samara State Economic University, 141 Sovetskoi Armii str., Samara, 443090 Russia

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 for Grubbs' 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.

Keywords: copula-function, tail dependence, upper-left and lower-right tail dependencies coefficients, symmetric copula, joint distribution function of standardized maximum and minimum, normal distribution.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:12, 56–72

UDC: 519.243
Received: 30.05.2014

Citation: L. K. Shiryaeva, “On tail dependence for Grubbs' copula-function”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 12, 66–83; Russian Math. (Iz. VUZ), 59:12 (2015), 56–72

Citation in format AMSBIB
\Bibitem{Shi15}
\by L.~K.~Shiryaeva
\paper On tail dependence for Grubbs' copula-function
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 12
\pages 66--83
\mathnet{http://mi.mathnet.ru/ivm9063}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 12
\pages 56--72
\crossref{https://doi.org/10.3103/S1066369X15120063}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84946402136}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. K. Shiryaeva, “On distrubution of Grubbs' statistics in case of normal sample with outlier”, Russian Math. (Iz. VUZ), 61:4 (2017), 72–88  mathnet  crossref  isi
    2. L. K. Shiryaeva, E. G. Repina, “O nekotorykh svoistvakh simmetrichnoi kopuly Grabbsa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 714–734  mathnet  crossref  elib
    3. L. K. Shiryaeva, “O trekhparametricheskoi kopula-funktsii Grabbsa”, Izv. vuzov. Matem., 2019, no. 3, 54–71  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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