Compute measures of extremal dependence for 2 variables.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  chi(data, nq = 100, qlim = NULL, alpha = 0.05, trunc = TRUE)
## S3 method for class 'chi'
summary(object, ...)
## S3 method for class 'summary.chi'
print(x, digits=3, ...)
## S3 method for class 'chi'
print(x, ...)
## S3 method for class 'chi'
plot(x, show=c("Chi"=TRUE,"ChiBar"=TRUE), lty=1,
cilty=2, col=1, spcases=TRUE, cicol=1, xlim=c(0, 1), ylimChi =
c(1, 1), ylimChiBar = c(1, 1), mainChi = "Chi", mainChiBar =
"Chi Bar", xlab = "Quantile", ylabChi =
expression(chi(u)), ylabChiBar = expression(bar(chi)(u)),
ask, ...)
## S3 method for class 'chi'
ggplot(data=NULL, mapping, xlab = "Quantile",
ylab=c("ChiBar" = expression(bar(chi)(u)), "Chi" = expression(chi(u))),
main=c("ChiBar" = "Chi Bar", "Chi" = "Chi"),
xlim = c(0, 1), ylim =list("Chi" = c(1, 1),"ChiBar" = c(1, 1)),
ptcol="blue",fill="orange",show=c("ChiBar"=TRUE,"Chi"=TRUE),
spcases = TRUE,plot., ..., environment)

data 
A matrix containing 2 numeric columns. 
nq 
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

trunc 
Logical flag indicating whether the estimates should be
truncated at their theoretical bounds. Defaults to 
x, object 
An object of class 
digits 
Number of digits for printing. 
show 
Logical, of length 2, names "Chi" and "ChiBar". Defaults to 
lty, cilty, col, cicol 
Line types and colours for the the estimated quantities and their confidence intervals. 
xlim, ylimChi, ylimChiBar 
Limits for the axes. 
mainChi, mainChiBar 
Main titles for the plots. 
xlab, ylabChi, ylabChiBar 
Axis labels for the plots. 
mapping, ylab, main, ylim, ptcol, fill, environment 
Arguments to ggplot methods. 
spcases 
Whether or not to plot special cases of perfect (positive and
negative) dependence and indpenendence. Defaults to 
plot. 
whether to plot to active graphics device. 
ask 
Whether or not to ask before reusing the graphics device. 
... 
Further arguments to be passed to methods. 
Computes the functions chi and chibar described by Coles, Heffernan and Tawn (1999). The limiting values of these functions as the quantile approaches 1 give an empirical measure of the type and strength of tail dependendce exhibited by the data.
A limiting value of ChiBar equal to 1 indicates Asymptotic Dependence, in which case the limiting value of Chi gives a measure of the strength of dependence in this class. A limiting value of ChiBar of less than 1 indicates Asymptotic Independence in which case Chi is irrelevant and the limiting value of ChiBar gives a measure of the strength of dependence.
The plot and ggplot methods show the ChiBar and Chi functions. In the case of the confidence interval for ChiBar excluding the value 1 for all of the largest quantiles, the plot of the Chi function is shown in grey.
An object of class chi
containing the following.
chi 
Values of chi and their estimated upper and lower confidence limits. 
chibar 
Values of chibar and their estimated upper and lower confidence limits. 
quantile 
The quantiles at which chi and chibar were evaluated. 
chiulb, chibarulb 
Upper and lower bounds for chi and chibar. 
When the data contain ties, the values of chi and chibar are
calculated by assigning distinct ranks to tied values using the rank
function with argument ties.method = "first"
. This results in the
values of chi and chibar being sensitive to the order in which the tied
values appear in the data.
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.
Janet E. Heffernan, Alec Stephenson, Harry Southworth
S. Coles, J. E. Heffernan and J. A. Tawn, Dependence measures for extreme values analyses, Extremes, 2, 339 – 365, 1999.
A. G. Stephenson. evd: Extreme Value Distributions, R News, 2, 2002.
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