qcbvnonpar {evd}

Non-parametric Estimates for Bivariate Quantile Curves

Description

Calculate or plot non-parametric estimates for quantile curves of bivariate extreme value distributions.

Usage

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], ...)

Arguments

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, 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

\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).

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)