POT (version 1.1-11)

tailind.test: 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)

Value

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

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.

Author

Mathieu Ribatet

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 \(c \rightarrow 0^{-}\) iff \(X\) and \(Y\) are asymptotically independent. Otherwise, the limit is \(F(t) = t\)

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)

##An 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))