tailind.test {POT}R Documentation

Testing for Tail Independence in Extreme Value Models

Description

Several tests for tail independence (e.g. asymptotic independence) for a bivariate extreme value distribution

Usage

tailind.test(data, c = -0.1, emp.trans = TRUE, chisq.n.class = 4)

Arguments

data A matrix with two columns given the data.
c A negative numeric. Must be close to zero to approximate accurately asymptotic results.
emp.trans Logical. If TRUE (the default), ``data'' is transformed to reverse exponential using empirical estimates. Otherwise, ``data'' is supposed to be reverse exponential distributed.
chisq.n.class A numeric given the number of classes for the Chi squared test.

Details

These tests are based on an asymptotic results shown by Falk and Michel (2006). Let (X,Y) be a random vector which follows in its upper tail a bivariate extreme value distribution with reverse exponential margins. The conditional distribution function of X+Y, given that X+Y>c, converges to F(t)=t^2, t in [0,1], if t tends to 0 iff X and Y are asymptotically independent. Otherwise, the limit is F(t) = t

Value

This function returns a table with the Neymann-Pearson, Fisher, Kolmogorov-Smirnov and Chi-Square statistics and the related p-values.

Author(s)

Mathieu Ribatet

References

Falk, M. and Michel, Rene (2006) Testing for tail independence in extreme value models. Annals of the Institute of Statistical Mathematics 58: 261–290

See Also

chimeas, specdens

Examples

##A total independence example
x <- rbvgpd(7000, alpha = 1, mar1 = c(0, 1, 0.25))
tailind.test(x)
##A asymptotically dependent example
y <- rbvgpd(7000, alpha = 0.75, model = "nlog", mar1 = c(0, 1, 0.25),
mar2 = c(2, 0.5, -0.15))
tailind.test(y)
##A perfect dependence example
z <- rnorm(7000)
tailind.test(cbind(z, 2*z - 5))

[Package POT version 1.0-1 Index]