Contains \(6\) datasets: PNS, PNN, NSN, PNNS,
winterdat and Leeds.frechet.
The dataset winterdat contains \(590\) (transformed) observations for
each of the five pollutants. Contains NAs.
Outliers have been removed according to Heffernan and Tawn (2004).
The following datasets have been obtained by applying transformations to winterdat.
Leeds.frechet contains \(590\) observations corresponding to the
daily maxima of five air pollutants transformed to unit Frechet scale.
NSN contains \(100\) observations in the \(3\)-dimensional
unit simplex for the daily maxima of nitrogen dioxide (NO2), sulfur dioxide (SO2)
and nitrogen oxide (NO).
PNN contains \(100\) observations in the \(3\)-dimensional
unit simplex for the daily maxima of particulate matter (PM10), nitrogen oxide (NO)
and nitrogen dioxide (NO2).
PNS contains \(100\) observations in the \(3\)-dimensional
unit simplex for the daily maxima of particulate matter (PM10), nitrogen oxide (NO)
and sulfur dioxide (SO2).
PNNS contains \(100\) observations in the \(4\)-dimensional
unit simplex for the daily maxima of particulate matter (PM10), nitrogen oxide (NO),
nitrogen dioxide (NO2) and sulfur dioxide (S02).
The transformation to unit Frechet margins of the raw data has been considered by Cooley et al (2010). Only the \(100\) data points with the largest radial components were kept.
Cooley, D.,Davis, R. A., and Naveau, P. (2010). The pairwise beta distribution: a flexible parametric multivariate model for extremes. Journal of Multivariate Analysis, 101, 2103--2117.
Heffernan, J. E., and Tawn, J. A. (2004). A conditional approach for multivariate extreme values. Journal of the Royal Statistical Society, Series B, Methodology, 66, 497--546