diplot: Threshold Selection: The Dispersion Index Plot

In POT: Generalized Pareto Distribution and Peaks Over Threshold

Threshold Selection: The Dispersion Index Plot

Description

The Dispersion Index Plot

Usage

diplot(data, u.range, main, xlab, ylab, nt = max(200, nrow(data)),
conf=0.95, ...)

Arguments

data	A matrix with two column. The first one represents the date of events (in a numeric format) and the second the data associated with those dates.
u.range	A numeric vector of length two giving the limit of threshold analyzed. If missing, default values are taken.
main	The title of the plot.
xlab, ylab	Labels for the x and y axis.
nt	The number of thresholds at which the dispersion index plot is evaluated.
conf	The confident coefficient for the plotted confidence intervals.
...	Other arguments to be passed to the plot function.

Details

According to the Extreme Value Theory, the number of exceedance over a high threshold in a fixed period - generally a year - must be distributed as Poisson process. As for a random variable Poisson distributed, the ratio of the variance and the mean is equal to 1, one can test if the ratio \code{DI} = var / mean differs from 1. Moreover, confidence levels for DI can be calculated by testing against a \chi^2 distribution with M-1 degree of freedom, M being the total number of fixed periods -generally the total number of years in the sample. So, the Poisson hypothesis is not rejected if the estimated DI is within the range

\left[ \frac{\chi^2_{\alpha/2, \code{M}-1}}{\code{M}-1}, \frac{\chi^2_{1 - \alpha/2, \code{M}-1} }{\code{M} - 1} \right]

Value

It returns invisibly a list with two components. The first one 'thresh' gives the thresholds analyzed. The second 'DI' gives the dispersion index relative to the threshold.

Author(s)

Mathieu Ribatet

References

Cunnane, C. (1979) Note on the poisson assumption in partial duration series model. Water Resource Research, 15(2) :489–494.

Examples

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
diplot(ardieres)

POT documentation built on Oct. 17, 2024, 5:06 p.m.