mev (version 2.1)

xdep.chi: Coefficient of tail correlation

Description

The coefficient of tail correlation \(\chi\) is $$\chi = \lim_{u \to 1} \frac{\Pr(F_1(X_1)>u, \ldots, F_D(X_D)>u)}{1-u}.$$ Asymptotically independent vectors have \(\chi = 0\). The estimator uses an estimator of the survival copula

Usage

xdep.chi(
  xdat,
  qlev = NULL,
  nq = 40,
  qlim = c(0.8, 0.99),
  estimator = c("emp", "betacop", "gpd", "hill"),
  confint = c("wald", "lrt"),
  level = 0.95,
  margtrans = c("emp", "none"),
  ties.method = "random",
  plot = TRUE,
  ...
)

Value

a data frame

• qlev: quantile level of estimates

• coef: point estimates

• lower: lower bound of confidence interval

• upper: lower bound of confidence interval

Arguments

xdat

an \(n\) by \(d\) matrix of multivariate observations

qlev

vector of percentiles between 0 and 1

nq

number of quantiles of the structural variable at which to form a grid; only used if u = NULL.

qlim

limits for the sequence u of the structural variable

estimator

string giving estimator to employ

confint

string indicating the type of confidence interval, one of "wald" or "lrt"

level

the confidence level required (default to 0.95).

margtrans

string giving the marginal transformation, one of emp for rank-based transformation or none if data are already on the uniform scale

ties.method

string indicating the type of method for rank; see rank for a list of options. Default to "random"

plot

logical; if TRUE, return a plot

...

additional arguments to taildep, currently ignored

Examples

if (FALSE) {
set.seed(765)
# Max-stable model
dat <- rmev(n = 1000, d = 2, param = 0.7, model = "log")
xdep.chi(dat, confint = 'wald')
}