Description Usage Arguments Details Value Note Author(s) References See Also Examples

Compute measures of extremal dependence for 2 variables.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
chi(data, nq = 100, qlim = NULL, alpha = 0.05, trunc = TRUE)
## S3 method for class 'chi'
summary(object, digits=3, ...)
## 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)),#"Chi(u)"
ylabChiBar = expression(bar(chi)(u)), #"Chi Bar(u)"
ask, ...)
``` |

`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. |

`spcases` |
Whether or not to plot special cases of perfect (positive and negative) dependence and indpenendence. Defaults to |

`ask` |
Whether or not to ask before reusing the graphics device. |

`...` |
Further arguments to be passed to methods. |

Computes the functions chi and chi-bar described by Coles,
Heffernan and Tawn. 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 the limiting value of ChiBar gives a measure of the strength of dependence.

The plot method shows the ChiBar and Chi functions. In the case of the
confidence interval for ChiBar excluding the value 1 for all of the largest
values of `Quantile`

, the plot of the Chi function is shown in grey.

An object of class `chi`

containing the following.

`chi ` |
Values of chi and their esitmated upper and lower confidence limits. |

`chibar ` |
Values of chibar and their esitmated upper and lower confidence limits. |

`quantile` |
The quantiles at which chi and chi-bar were evaluated. |

`chiulb, chibarulb` |
Upper and lower bounds for chi and chi-bar. |

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.

1 2 3 4 5 6 7 8 9 |

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