qcbvnonpar {evd} | R Documentation |
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"), convex = FALSE, madj = 0, plot = FALSE, add = FALSE, lty = 1, lwd = 1, col = 1, xlim, ylim, xlab, ylab, ...)
p |
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 |
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 . |
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 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).
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.
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)