Mean residual life plot

Description

Calculate mean residual life and plot it to aid the identification of a threshold over which to fit a generalized Pareto distribution

Usage

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mrl(data, umin = min(data), umax = max(data) - 0.1, nint = 100,
alpha=.050)
## S3 method for class 'mrl'
print(x, ...)
## S3 method for class 'summary.mrl'
print(x, ...)
## S3 method for class 'mrl'
summary(object, ...)
## S3 method for class 'mrl'
plot(x, xlab="Threshold", ylab="Mean excess", ...)
## S3 method for class 'mrl'
ggplot(data, mapping, xlab="Threshold", ylab="Mean excess",
main=NULL, fill="orange", col="blue", rug=TRUE, addNexcesses = TRUE, textsize=4,
..., environment)

Arguments

data

A numeric vector.

umin

The minimum value over which to threshold the data.

umax

The maximum value over which to threshold the data.

nint

The number of points at which to compute the plot.

alpha

Used to determine coverage of confidence interval to plot. Defaults to plotting a 95% interval.

x, object

Arguments to print, summary and plot functions.

xlab

Label for the x-axis. Defaults to xlab="Threshold".

ylab

Label for the y-axis. Defaults to ylab="Mean excess".

...

Optional arguments to plot.

col

Colour of the line on the MRL plot.

rug

Whether to add a rug to the plot. Defaults to rug=TRUE.

fill

Colour of the pointwise confidence region on the MRL plot.

main

Main title.

addNexcesses

Whether to annotate the plot with the numbers of excesses over increasing thresholds. Defaults to addNexcesses=TRUE.

textsize

Size of text on the plot (ggplot). Defaults to textsize=4.

mapping, environment

Not used.

Details

Threshold choice for the fitting of the GPD is guided by the shape of the Mean Residual Life plot. A threshold which is suitably high will have a corresponding mrl plot which is approximately linear in shape above the threshold (up to sampling variation).

Value

A list with two components. data is the original data, mrl is a matrix containing information to produce the mean residual life plot.

Note

The function was originally written by Stuart Coles and appears in the ismev package. This version modified by Harry Southworth to allow more control over the appearance of the plot.

Author(s)

Janet E. Heffernan, Harry Southworth

References

S. Coles, An Introduction to Statistical Modeling of Extreme Values, Springer, 2001

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