tail_plot function

Plot of an Empirical Surival Function with Smith Estimator

Plot an empirical tail survival function, possibly overlaid with the Smith estimator.

tail_plot(x, threshold, shape = NULL, scale = NULL,
          q = NULL, length.out = 129, lines.args = list(),
          log = "xy", xlim = NULL, ylim = NULL,
          xlab = "x", ylab = "Tail probability at x", ...)

Arguments

• x: numeric vector of data.

• threshold: numeric(1) giving the threshold $u$ above which the tail (starts and) is to be plotted.

• shape: NULL or the GPD shape parameter $xi$

  (typically obtained via fit_GPD_MLE()).

• scale: NULL or the GPD shape parameter $beta$

  (typically obtained via fit_GPD_MLE()).

• q: NULL, numeric(1) or numeric vector of evaluationn points of the Smith estimator (semi-parametric GPD-based tail estimator in the POT method). If NULL, the evaluation points are determined internally as an equidistant sequence of length length.out between the smallest and largest exceedance (taken equidistant in log-scale if log contains "x"). If numeric(1), then the behavior is similar to NULL

  with the exception that the plot is extended to the right of the largest exceedance if q is larger than the largest exceedance.

• length.out: length of q.

• lines.args: list of arguments passed to the underlying lines().

• log: character indicating whether logarithmic axes are to be used.

• xlim: x-axis limits.

• ylim: y-axis limits.

• xlab: x-axis label.

• ylab: y-axis label.

• ...: additional arguments passed to the underlying plot().

Returns

If both shape and scale are provided, tail_plot()

overlays the empirical tail survival function estimator (evaluated at the exceedances) with the corresponding GPD. In this case, tail_plot() invisibly returns a list with two two-column matrices, one containing the x-values and y-values of the empirical survival distribution estimator and one containing the x-values and y-values of the Smith estimator. If shape or scale are NULL, tail_plot() invisibly returns a two-column matrix with the x-values and y-values of the empirical survival distribution estimator.

Author(s)

Marius Hofert

Examples

## Generate losses to work with
set.seed(271)
X <- rt(1000, df = 3.5) # in MDA(H_{1/df}); see MFE (2015, Section 16.1.1)

## Threshold (see ?dGPDtail, for example)
u <- 1.5 # threshold

## Plots of empirical survival distribution functions (overlaid with Smith estimator)
tail_plot(X, threshold = u, log = "", type = "b") # => need log-scale
tail_plot(X, threshold = u, type = "s") # as a step function
fit <- fit_GPD_MLE(X[X > u] - u) # fit GPD to excesses (POT method)
tail_plot(X, threshold = u, # without log-scale
          shape = fit$par[["shape"]], scale = fit$par[["scale"]], log = "")
tail_plot(X, threshold = u, # highlights linearity
          shape = fit$par[["shape"]], scale = fit$par[["scale"]])