R: Non-parametric Estimates for Bivariate Quantile Curves

qcbvnonpar {evd} | R Documentation

## 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

{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)

[Package evd version 2.3-4 Index]