chi: Measures of extremal dependence

Description

Compute measures of extremal dependence for 2 variables.

Usage

chi(data, nq = 100, qlim = NULL, alpha = 0.05, trunc = TRUE)
## S3 method for class 'chi':
print(x, ...)
## S3 method for class 'chi':
summary(object, digits=3, ...)
## S3 method for class 'chi':
plot(x, which=1:2, lty=1, cilty=2, col=1, spcases=FALSE,
                   cicol=1, xlim=c(0, 1), ylim1=c(-1, 1), ylim2=c(-1, 1),
                   main1="Chi", main2="Chi Bar", xlab="Quantile",
                   ylab1=expression(chi),
                   ylab2=expression(bar(chi)),
                   ask=nb.fig < length(which) && dev.interactive(), ...)

Arguments

data

A matrix containing 2 numeric columns.

The number of quantiles at which to evaluate the dependence measures.

qlim

The minimum and maximum quantiles at which to do the evaluation.

alpha

The size of the confidence interval to be used. Defaults to alpha = 0.05.

trunc

Logical flag indicating whether the estimates should be truncated at their theoretical bounds. Defaults to trunc = TRUE.

x, object

An object of class chi.

digits

Number of digits for printing.

which

Which plot to do: 1 results in a plot of chi, 2 in a plot of chi bar. Defaults to which = 1:2.

lty, cilty, col, cicol

Line types and colours for the the estimated quantities and thier confidence intervals.

xlim, ylim1, ylim2

Limits for the axes.

main1, main2

Main titles for the plots.

xlab, ylab1, ylab2

Axis labels for the plots.

spcases

Whether or not to plot special cases. Defaults to FALSE.

ask

Whether or not to ask before reusing the graphics device.

...

Further arguments to be passed to methods.

Value

An object of class chi containing the following.
chiValues of chi and their esitmated upper and lower confidence limits.
chibarValues of chibar and their esitmated upper and lower confidence limits.
quantileThe quantiles at which chi and chi-bar were evaluated.
chiulb, chibarulbUppwer and lower bounds for chi and chi-bar.

Details

Computes the values chi and chi-bar described by Coles, Heffernan and Tawn. The code is a fairly simple reorganization of code written by Janet E. Heffernan and Alec Stephenson and which appears in the chiplot function in the evd package.

References

S. Coles, J. E. Heffernan and J. A. Tawn, Dependence measures for extreme values analyses, Extremes, 2, 339 -- 365, 1999

Examples

Run this code

D <- liver[liver$dose == "D",]
chiD <- chi(D[, 5:6])
plot(chiD)

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