On Necessary Conditions for Dependence Parameters of Minimum and Maximum Value Distributions Based on n-Variate FGM Copula

抄録

This paper deals with the minimum and maximum value distributions based on the n-variate FGM copula with one dependence parameter. The ranges of dependence parameters are theoretically determined so that the probability density function always takes a non-negative value. However, the closed-form conditions of the ranges for the dependence parameters have not been known in the literature. In this paper, we newly provide the necessary conditions of the ranges of the dependence parameters for the minimum and maximum value distributions which are derived from FGM copula, and show the asymptotic properties of the ranges.