hill function

Create Hill Plot

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

hill(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 Also

shape, quant

Examples

## Not run: data(danish)
## Not run: hill(danish)
# Hill plot of heavy-tailed Danish fire insurance data 
## Not run: hill(danish, option = "quantile", end = 500, p = 0.999)
# Hill plot of estimated 0.999 quantile of Danish fire insurance data