depchi {IndTestPP} | R Documentation |
Estimating extremal dependence coefficientes
Description
This function estimates and plots the extremal dependence functions
and
against a grid of values in [0,1]
to analyse the extremal dependence of two variables.
Usage
depchi(X, Y, thresval = c(0:99)/100, tit = "", indgraph = TRUE, bothest = TRUE,
xlegend = "topleft",mfrow=c(1,2),...)
Arguments
X |
Numeric vector. Values of the first variable. |
Y |
Numeric vector. Values of the second variable. |
thresval |
Numeric vector. Grid values where the functions |
tit |
Character string. A title for the plots. |
indgraph |
Logical flag. If it is TRUE, plots are shown in separate windows.
If it is FALSE, the layout in |
bothest |
Logical flag. If it is TRUE, two estimated coefficientes (for X given Y and for Y given X) are displayed in the same plot. Otherwise, only the coefficient for Y given X is plotted. |
xlegend |
Optional. Label "topleft","bottomright", etc. Position where the legend on the graph will be located. |
mfrow |
Optional. A vector of the form c(2, 1) or c(1,2). It gives the layout to draw the two figures in the function. |
... |
Further arguments to be passed to the function |
Details
The extremal dependence between two variables X and Y
is the tendency for one variable to be large, given that the other one is large.
The extremal dependence coefficients and
are defined as
where
and (U,V) are the
transformed uniform marginals of the variables X and Y.
where
.
The function plots and
. These graphs
can be used to estimate
and
, the limits of the functions.
In the
plot, the expected behaviour under independence of X and Y is also plotted.
is on the scale [0, 1], with the set (0, 1] corresponding to asymptotic
dependence, and the measure
falls within the range [-1, 1], with the set [-1, 1)
corresponding to asymptotic independence. See Coles et al. (1999) for more details on the definition
and interpretation of these indexes.
Value
A list with elements
chiX |
Estimated |
chiY |
Estimated |
chiBX |
Estimated |
chiBY |
Estimated |
PX |
Estimation of the probabilities |
PY |
Estimation of the probabilities |
PXY |
Estimation of the probabilities |
thresval |
Input argument. |
References
Coles, S., Heffernan, J. and Tawn, J. (1999) Dependence measures for extreme value analysis. Extremes, 2, 339-365.
See Also
Examples
data(TxBHZ)
aux<-depchi(X=TxBHZ$TxZ,Y=TxBHZ$TxH, thresval = c(0:99)/100,
tit = "Tx Zaragoza and Tx Huesca", xlegend = "bottom",indgraph="FALSE")