A vector of lower tail probabilities. One quantile curve is
calculated or plotted for each probability.
data
A matrix or data frame with two columns, which may contain
missing values.
epmar
If TRUE, an empirical transformation of the
marginals is performed in preference to marginal parametric
GEV estimation, and the nsloc arguments are ignored.
nsloc1, nsloc2
A data frame with the same number of rows as
data, for linear modelling of the location parameter on the
first/second margin. The data frames are treated as covariate
matrices, excluding the intercept. A numeric vector can be given
as an alternative to a single column data frame.
mint
An integer m. Quantile curves are plotted or
calculated using the lower tail probabilities p^m.
method, kmar
Arguments for the non-parametric estimate of the
dependence function. See abvnonpar.
convex, madj
Other arguments for the non-parametric
estimate of the dependence function.
plot
Logical; if TRUE the data is plotted along
with the quantile curves. If plot and add are
FALSE (the default), the arguments following add
are ignored.
add
Logical; add quantile curves to an existing data plot?
The existing plot should have been created using either
qcbvnonpar or plot.bvevd, the latter of
which can plot quantile curves for parametric fits.
lty, lwd
Line types and widths.
col
Line colour.
xlim, ylim
x and y-axis limits.
xlab, ylab
x and y-axis labels.
...
Other high-level graphics parameters to be passed to
plot.
Details
Let G be a fitted bivariate distribution function with
margins G_1 and G_2. A quantile curve for a fitted
distribution function G at lower tail probability p is defined
by
Q(G, p) = {(y_1,y_1):G(y_1,y_2) = p}.
For bivariate extreme value distributions, it consists
of the points
{G_1^{-1}(p_1),G_2^{-1}(p_2))}
where p_1 = p^{t/A(t)} and p_2 = p^{(1-t)/A(t)},
with A being the estimated dependence function defined
in abvevd, and where t lies in the interval
[0,1].
By default the margins G_1 and G_2 are modelled using
estimated generalized extreme value distributions.
For non-stationary generalized extreme value margins the plotted
data are transformed to stationarity, and the plot corresponds
to the distribution obtained when all covariates are zero.
If epmar is TRUE, empirical transformations
are used in preference to generalized extreme value models.
Note that the marginal empirical quantile functions are
evaluated using quantile, which linearly
interpolates between data points, hence the curve will not
be a step function.
The idea behind the argument code{mint} = m is that if
G is fitted to a dataset of componentwise maxima, and the
underlying observations are iid distributed according
to F, then if m is the size of the blocks over which the
maxima were taken, approximately F^m = G, leading
to Q(F, p) = Q(G, p^m).
Value
qcbvnonpar calculates or plots non-parametric quantile
curve estimates for bivariate extreme value distributions.
If p has length one it returns a two column matrix
giving points on the curve, else it returns a list of
such matrices.
See Also
abvevd, abvnonpar,
plot.bvevd
Examples
bvdata <- rbvevd(100, dep = 0.7, model = "log")
qcbvnonpar(c(0.9,0.95), data = bvdata, plot = TRUE)
qcbvnonpar(c(0.9,0.95), data = bvdata, epmar = TRUE, plot = TRUE)