The Dispersion Index Plot
diplot(data, u.range, main, xlab, ylab, nt = max(200, nrow(data)),
conf=0.95, ...)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.
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.
A numeric vector of length two giving the limit of threshold analyzed. If missing, default values are taken.
The title of the plot.
Labels for the x and y axis.
The number of thresholds at which the dispersion index plot is evaluated.
The confident coefficient for the plotted confidence intervals.
Other arguments to be passed to the plot function.
Mathieu Ribatet
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
$$\left[ \frac{\chi^2_{\alpha/2, \code{M}-1}}{\code{M}-1},
\frac{\chi^2_{1 - \alpha/2, \code{M}-1} }{\code{M} - 1} \right]$$
Cunnane, C. (1979) Note on the poisson assumption in partial duration series model. Water Resource Research, 15(2) :489--494.
data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
diplot(ardieres)
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