POT (version 1.1-11)

tcplot: Threshold Selection: The Threshold Choice Plot

Description

Plots of parameter estimates at various thresholds for peaks over threshold modelling, using the Generalized Pareto or Point Process representation.

Usage

tcplot(data, u.range, cmax = FALSE, r = 1,
    ulow = -Inf, rlow = 1, nt = 25, which = 1:npar, conf = 0.95,
    lty = 1, lwd = 1, type = "b", cilty = 1, ask = nb.fig <
    length(which) && dev.interactive(), ...)

Value

A list is invisibly returned. Each component is a matrix with three columns giving parameter estimates and confidence limits.

Arguments

data

A numeric vector.

u.range

A numeric vector of length two, giving the limits for the thresholds at which the model is fitted.

cmax

Logical; if FALSE (the default), the models are fitted using all exceedances over the thresholds. If TRUE, the models are fitted using cluster maxima.

r, ulow, rlow

Arguments used for the identification of clusters of exceedances. Ignored if cmax is FALSE (the default).

nt

The number of thresholds at which the model is fitted.

which

If a subset of the plots is required, specify a subset of the numbers 1:npar, where npar is the number of parameters.

conf

The (pointwise) confidence coefficient for the plotted confidence intervals. Use zero to suppress.

lty, lwd

The line type and width of the line connecting the parameter estimates.

type

The form taken by the line connecting the parameter estimates and the points denoting these estimates. Possible values include "b" (the default) for points joined by lines, "o" for over plotted points and lines, and "l" for an unbroken line with no points.

cilty

The line type of the lines depicting the confidence intervals.

ask

Logical; if TRUE, the user is asked before each plot.

...

Other arguments to be passed to the model fit function fitgpd.

Author

Stuart Coles and Alec Stephenson

Details

For each of the nt thresholds a peaks over threshold model is fitted using the function fitgpd. The maximum likelihood estimates for the shape and the modified scale parameter (modified by subtracting the shape multiplied by the threshold) are plotted against the thresholds. If the threshold u is a valid threshold to be used for peaks over threshold modelling, the parameter estimates depicted should be approximately constant above u.

References

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

See Also

fitgpd, mrlplot

Examples

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
flows <- ardieres[, "obs"]
par(mfrow=c(1,2))
tcplot(flows, u.range = c(0, 15) )