BiCopChiPlot {VineCopula} | R Documentation |
Chi-plot for Bivariate Copula Data
Description
This function creates a chi-plot of given bivariate copula data.
Usage
BiCopChiPlot(u1, u2, PLOT = TRUE, mode = "NULL", ...)
Arguments
u1 , u2 |
Data vectors of equal length with values in |
PLOT |
Logical; whether the results are plotted. If |
mode |
Character; whether a general, lower or upper chi-plot is
calculated. Possible values are |
... |
Additional plot arguments. |
Details
For observations the chi-plot is based on the following two quantities: the
chi-statistics
and the lambda-statistics
where ,
and
are the empirical distribution functions
of the uniform random variables
and
and of
, respectively. Further,
and
.
These quantities only depend on the ranks of the data and are scaled to the
interval .
measures a distance of a data point
to the center of the
bivariate data set, while
corresponds to a correlation
coefficient between dichotomized values of
and
. Under
independence it holds that
and
asymptotically, i.e., values of
close to zero indicate independence—corresponding to
.
When plotting these quantities, the pairs of will tend to be located above zero for
positively dependent margins and vice versa for negatively dependent
margins. Control bounds around zero indicate whether there is significant
dependence present.
If mode = "lower"
or "upper"
, the above quantities are
calculated only for those 's and
's which are
smaller/larger than the respective means of
u1
and
u2
.
Value
lambda |
Lambda-statistics (x-axis). |
chi |
Chi-statistics (y-axis). |
control.bounds |
A 2-dimensional vector of bounds
|
Author(s)
Natalia Belgorodski, Ulf Schepsmeier
References
Abberger, K. (2004). A simple graphical method to explore tail-dependence in stock-return pairs. Discussion Paper, University of Konstanz, Germany.
Genest, C. and A. C. Favre (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12 (4), 347-368.
See Also
BiCopMetaContour()
, BiCopKPlot()
,
BiCopLambda()
Examples
## chi-plots for bivariate Gaussian copula data
# simulate copula data
fam <- 1
tau <- 0.5
par <- BiCopTau2Par(fam, tau)
cop <- BiCop(fam, par)
set.seed(123)
dat <- BiCopSim(500, cop)
# create chi-plots
op <- par(mfrow = c(1, 3))
BiCopChiPlot(dat[,1], dat[,2], xlim = c(-1,1), ylim = c(-1,1),
main="General chi-plot")
BiCopChiPlot(dat[,1], dat[,2], mode = "lower", xlim = c(-1,1),
ylim = c(-1,1), main = "Lower chi-plot")
BiCopChiPlot(dat[,1], dat[,2], mode = "upper", xlim = c(-1,1),
ylim = c(-1,1), main = "Upper chi-plot")
par(op)