qcbvnonpar | 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",
"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], ...)
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 |
nsloc1 , nsloc2 |
A data frame with the same number of rows as
|
mint |
An integer |
method , kmar |
Arguments for the non-parametric estimate of the
dependence function. See |
convex , madj |
Other arguments for the non-parametric estimate of the dependence function. |
plot |
Logical; if |
add |
Logical; add quantile curves to an existing data plot?
The existing plot should have been created using either
|
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
|
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)
.
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.
abvevd
, abvnonpar
,
plot.bvevd
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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