FEATURES OF COPULA FUNCTIONS, BASED ON JOINT DISTRIBUTION OF GRUBBS`S TESTS STATISTICS


Shiryaeva L.K.

The author considers unilateral Grubbs`s tests statistics, i.e. standardized maximum and minimum calculated by the normal sample. Because of joint distribution of these statistics the author develops a new one-parameter copula function by inversion and the graphs of the simulated values of this copula. It is proved that Grubbs’s copula allows describing the negative relationship between random variables. The author develops approximation for Spearman’s rank correlation coefficient of this copula and makes model calculations of the joint distribution function of random variables when their relationship is described by Grubbs`s copula, and each of the random variables has Cauchy`s distribution. Keywords: copula function, joint distribution of unilateral Grubbs`s tests, scatterplots, Spearman`s rank correlation coefficient, normal distribution, standardized minimum and maximum, Monte Carlo method.

Lyudmila K. Shiryaeva, candidate of Physical and Mathematical Sciences, Associate Professor. Samara State University of Economics.


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