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Create Excess Plots

Source: R/excess_plot.R
excess_plot.Rd

`excess_plot()` creates a mean or median excess plot as a side-effect and returns the data frame invisibly.

Usage

excess_plot(
  x,
  method = c("mean", "median"),
  mode = c("exact", "interpolate"),
  show_plot = TRUE,
  ...
)

Arguments

x

a numeric vector.

method

"mean" or "median".

mode

"exact" or "interpolate".

show_plot

logical.

...

optional arguments to be passed to the plot() function, such as main, xlab, ylab, col, etc.

Value

`excess_plot()` returns a data frame containing the data used for plotting. If show_plot is TRUE, the data frame is returned invisibly.

Details

`excess_plot()` generates a mean or median excess plot, which is a key tool for visually assessing the tail behavior of a distribution.

Mean Excess Plot (MEP) represents the function \(e(u) = \mathrm{E}[\;\mathrm{X} - u\mid\mathrm{X} > u\;]\), i.e., the average of all exceedances over a given threshold u. This plot helps in identifying the type of tail behavior. An upward trend suggests a heavy-tailed distribution, a flat trend indicates an exponential distribution, and a downward trend points to a light-tailed distribution.

Median Excess Plot is similar to the MEP, but uses the median of the exceedances instead of the mean. This makes the plot more robust to outliers.

Examples

# Create a mean excess plot
excess_plot(x = rexp(100))


# Create a median excess plot without showing the plot
excess_data <- excess_plot(x = rexp(100), method = "median", show_plot = FALSE)

# Customize the plot appearance
excess_plot(x = rexp(100), col = "maroon", main = "Mean Excess Plot")