hillPlot {QRMlib}R Documentation

Create Hill Plot

Description

Plot the Hill estimate of the tail index of heavy-tailed data, or of an associated quantile estimate.

Usage

hillPlot(data, option = c("alpha", "xi", "quantile"), start = 15, 
   end = NA, reverse = FALSE, 
   p = NA, ci = 0.95, auto.scale = TRUE, labels = TRUE, ...)

Arguments

data data vector
option whether "alpha", "xi" (1/alpha) or "quantile" (a quantile estimate) should be plotted
start lowest number of order statistics at which to plot a point
end highest number of order statistics at which to plot a point
reverse whether plot is to be by increasing threshold (TRUE) or increasing number of order statistics (FALSE)
p probability required when option "quantile" is chosen
ci probability for asymptotic confidence band; for no confidence band set ci to zero
auto.scale whether or not plot should be automatically scaled; if not, xlim and ylim graphical parameters may be entered
labels whether or not axes should be labelled
... other graphics parameters

Details

This plot is usually calculated from the alpha perspective. For a generalized Pareto analysis of heavy-tailed data using the gpd function, it helps to plot the Hill estimates for xi. See pp. 286-289 in QRM. Especially note that Example 7.28 suggests the best estimates occur when the threshold is very small, perhaps 0.1 statistics in a sample of size 1000. Hence you should NOT be using a 95 estimates.

Value

None

Author(s)

documentation by Scott Ulman for R-language distribution

See Also

xiplot, plotTail

Examples

data(danish);
#Run hillPlot to show what happens with the Hill Plot.  
#See Example 7.27, p. 287 in QRM
hillPlot(danish, option = "alpha", start = 5, end = 250, p = 0.99);
hillPlot(danish, option = "alpha", start = 5, end = 60, p = 0.99);

[Package QRMlib version 1.4.4 Index]