hill {evir}

Create Hill Plot

Description

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

Usage

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