hillPlot {QRMlib} | R Documentation |
Plot the Hill estimate of the tail index of heavy-tailed data, or of an associated quantile estimate.
hillPlot(data, option = c("alpha", "xi", "quantile"), start = 15, end = NA, reverse = FALSE, p = NA, ci = 0.95, auto.scale = TRUE, labels = TRUE, ...)
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 |
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.
None
documentation by Scott Ulman for R-language distribution
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);