Cumulative distribution function of bivariate logistic model

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Description

Glog is cumulative distribution function of bivariate logistic model

Usage

1
Glog(x,y,alpha) 

Arguments

x

X variable with Frechet scale

y

Y variable with Frechet scale

alpha

dependence parameter between X and Y variables

Details

The bivariate logistic distribution function with parameter alpha is

G(x,y)=exp(-[x^(-1/alpha)+y^(-1/alpha)]^(alpha))

where 0 < alpha <= 1. Complete dependence is obtained in the limit as alpha approaches zero. Independence is obtained when alpha = 1. Note that x and y are assumed to follow the Frechet distribution for easy demonstration, so that G(z)=exp(-1/z), where z=x or y. However, this implies no loss of generality of the characterization of the bivariate extreme value distribution, since any other marginal distributions, whose extremal properties are determined by the univariate characterizations (GEV or GPD), can always be transformed into the standard Frechet form.

Value

Glog gives the distribution function value of x and y specified on a Frechet scale.

References

Coles, S.G. (2001), An introduction to statistical modelling of extreme values, Springer, London.