Calculate or plot non-parametric estimates for quantile curves of bivariate extreme value distributions.
qcbvnonpar(p = seq(0.75, 0.95, 0.05), data, epmar = FALSE, nsloc1 =
NULL, nsloc2 = NULL, mint = 1, method = c("cfg", "pickands",
"tdo"), convex = FALSE, madj = 0, kmar = NULL, plot = FALSE,
add = FALSE, lty = 1, lwd = 1, col = 1, xlim = range(data[,1],
na.rm = TRUE), ylim = range(data[,2], na.rm = TRUE), xlab =
colnames(data)[1], ylab = colnames(data)[2], …)A vector of lower tail probabilities. One quantile curve is calculated or plotted for each probability.
A matrix or data frame with two columns, which may contain missing values.
If TRUE, an empirical transformation of the
marginals is performed in preference to marginal parametric
GEV estimation, and the nsloc arguments are ignored.
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.
An integer \(m\). Quantile curves are plotted or calculated using the lower tail probabilities \(p^m\).
Arguments for the non-parametric estimate of the
dependence function. See abvnonpar.
Other arguments for the non-parametric estimate of the dependence function.
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.
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.
Line types and widths.
Line colour.
x and y-axis limits.
x and y-axis labels.
Other high-level graphics parameters to be passed to
plot.
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.
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
$$\left\{G_1^{-1}(p_1),G_2^{-1}(p_2))\right\}$$
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 \(Q(F, p) = Q(G, p^m)\).
# NOT RUN {
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)
# }
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