atvnonpar {evd} | R Documentation

## Non-parametric Estimates for Dependence Functions of the Trivariate Extreme Value Distribution

### Description

Calculate or plot non-parametric estimates for the dependence function A of the trivariate extreme value distribution.

### Usage

    atvnonpar(x = rep(1/3,3), data, nsloc1 = NULL, nsloc2 = NULL, nsloc3 = NULL,
        method = c("pickands", "deheuvels", "hall"), plot = FALSE,
        col = heat.colors(12), blty = 0, grid = if(blty) 150 else 50,
        lower = 1/3, ord = 1:3, lab = as.character(1:3), lcex = 1)

### Arguments

`x` | A vector of length three or a matrix with three columns, in which case the dependence function is evaluated across the rows (ignored if plot is `TRUE`). The elements/rows of the vector/matrix should be positive and should sum to one, or else they should have a positive sum, in which case the rows are rescaled and a warning is given. A(1/3,1/3,1/3) is returned by default since it is often a useful summary of dependence.
`data` | A matrix or data frame with three columns, which may contain missing values.
`nsloc1, nsloc2, nsloc3` | A data frame with the same number of rows as `data`, for linear modelling of the location parameter on the first/second/third 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.
`method` | The estimation method; a character string. Must be either `"pickands"` (the default), `"deheuvels"` or `"hall"` (or any unique partial match). The three estimators are very similar, and may not be distinguishable when plotted.
`plot` | Logical; if `TRUE` the function is plotted. The minimum (evaluated) value is returned invisibly. If `FALSE` (the default), the following arguments are ignored.
`col` | A list of colours (see `image`). The first colours in the list represent smaller values, and hence stronger dependence. Each colour represents an equally spaced interval between `lower` and one.
`blty` | The border line type, for the border that surrounds the triangular image. By default `blty` is zero, so no border is plotted. Plotting a border leads to (by default) an increase in `grid` (and hence computation time), to ensure that the image fits within it.
`grid` | For plotting, the function is evaluated at `grid^2` points.
`lower` | The minimum value for which colours are plotted. By default `lower` = 1/3 as this is the theoretical minimum of the dependence function of the trivariate extreme value distribution.
`ord` | A vector of length three, which should be a permutation of the set {1,2,3}. The points (1,0,0), (0,1,0) and (0,0,1) (the vertices of the simplex) are depicted clockwise from the top in the order defined by `ord`.
`lab` | A character vector of length three, in which case the `i`th margin is labelled using the `i`th component, or `NULL`, in which case no labels are given. By default, `lab` is `as.character(1:3)`. The actual location of the margins, and hence the labels, is defined by `ord`.
`lcex` | A numerical value giving the amount by which the labels should be scaled relative to the default. Ignored if `lab` is `NULL`.

### Value

`atvnonpar` calculates or plots a non-parametric estimate of the dependence function of the trivariate extreme value distribution.

### Note

The rows of `data` that contain missing values are not used in the estimation of the dependence structure, but every non-missing value is used in estimating the generalized extreme value margins.

The dependence function of the trivariate extreme value distribution is defined in `atvpar`. The function `atvpar` calculates and plots dependence functions of trivariate logistic and trivariate asymmetric logistic models.

### See Also

`atvpar`, `abvnonpar`, `fgev`

### Examples

    s3pts <- matrix(rexp(30), nrow = 10, ncol = 3)
    s3pts <- s3pts/rowSums(s3pts)
    sdat <- rmvevd(100, dep = 0.6, model = "log", d = 3)
    atvnonpar(s3pts, sdat)

    ## Not run: atvnonpar(data = sdat, plot = TRUE)
    ## Not run: atvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3])
    ## Not run: atvpar(dep = 0.6, model = "log", plot = TRUE)
    ## Not run: atvpar(dep = 0.6, model = "log", plot = TRUE, blty = 1)

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