The empirical mean residual life plot.
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), ...)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.
A numeric vector.
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.
Plot title.
x and y axis labels.
The number of thresholds at which the mean residual life plot is evaluated.
Arguments passed to matplot. The first
and last elements of lty correspond to the lower and
upper confidence limits respectively. Use zero to supress.
The (pointwise) confidence coefficient for the plotted confidence intervals.
Other arguments to be passed to matplot.
Stuart Coles and Alec Stephenson
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.
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.
fitgpd, matplot,
tcplot
data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
flows <- ardieres[, "obs"]
mrlplot(flows)
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