Geodesic
On tail dependence for Grubbs' copula-function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2015), pp. 66-83

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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
Mots-clés : normal distribution. 
@article{IVM_2015_12_a5,
     author = {L. K. Shiryaeva},
     title = {On tail dependence for {Grubbs'} copula-function},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--83},
     publisher = {mathdoc},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_12_a5/}
}
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L. K. Shiryaeva. On tail dependence for Grubbs' copula-function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2015), pp. 66-83. http://geodesic.mathdoc.fr/item/IVM_2015_12_a5/