# tailind.test: Testing for Tail Independence in Extreme Value Models In POT: Generalized Pareto Distribution and Peaks Over Threshold

## Description

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

## Usage

 `1` ```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.

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

`chimeas`, `specdens`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```##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)) ```