Description Usage Arguments Details Value References See Also Examples

This function estimates and plots the extremal dependence functions
*χ(u)* and *\bar χ(u)* against a grid of values in [0,1]
to analyse the extremal dependence of two variables.

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`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 |

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 *χ* and *\bar χ* are defined as
*χ= \lim_{u \to 1} χ(u)* where *χ(u)= P(U>u |V>u)* and (U,V) are the
transformed uniform marginals of the variables X and Y.

*\bar χ= \lim_{u \to 1} \bar χ(u)* where *\bar χ(u)= 2log P(U>u)/log P(U>u, V>u)-1*.

The function plots *χ(u)* and *\bar χ(u)*. These graphs
can be used to estimate *\hat χ* and *\widehat{\bar χ}*, the limits of the functions.
In the *χ (u)* plot, the expected behaviour under independence of X and Y is also plotted.

*χ* is on the scale [0, 1], with the set (0, 1] corresponding to asymptotic
dependence, and the measure *\bar χ* 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.

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. |

Coles, S., Heffernan, J. and Tawn, J. (1999) Dependence measures for extreme value analysis. Extremes, 2, 339-365.

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