mrlplot {POT}

Threshold Selection: The Empirical Mean Residual Life Plot

Description

The empirical mean residual life plot.

Usage

mrlplot(data, u.range, main, xlab, ylab, nt = max(100, length(data)),
lty = rep(1,3), col = c('grey', 'black', 'grey'), conf = 0.95, lwd = c(1,
1.5, 1), ...) 

Arguments

data

A numeric vector.

u.range

A numeric vector of length two, giving the limits for the thresholds at which the mean residual life plot is evaluated. If u.range is not given, sensible defaults are used.

main

Plot title.

xlab, ylab

x and y axis labels.

nt

The number of thresholds at which the mean residual life plot is evaluated.

lty, col, lwd

Arguments passed to matplot. The first and last elements of lty correspond to the lower and upper confidence limits respectively. Use zero to supress.

conf

The (pointwise) confidence coefficient for the plotted confidence intervals.

...

Other arguments to be passed to matplot.

Details

The empirical mean residual life plot is the locus of points

\left(u,\frac{1}{n_u} \sum\nolimits_{i=1}^{n_u} (x_{(i)} - u) \right)

where x_{(1)}, \dots, x_{(n_u)} are the n_u observations that exceed the threshold u. If the exceedances of a threshold u_0 are generalized Pareto, the empirical mean residual life plot should be approximately linear for u > u_0.

The confidence intervals within the plot are symmetric intervals based on the approximate normality of sample means.

Value

A list with components x and y is invisibly returned. The components contain those objects that were passed to the formal arguments x and y of matplot in order to create the mean residual life plot.

Author(s)

Stuart Coles and Alec Stephenson

References

Coles, S. (2001) An Introduction to Statistical Modelling of Extreme Values. Springer Series in Statistics. London.

Embrechts, P., Kl\"uppelberg, C., and Mikosch, T. (1997) Modelling Extremal Events for Insurance and Finance.

See Also

fitgpd, matplot, tcplot

Examples

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
flows <- ardieres[, "obs"]
mrlplot(flows)