# amvnonpar: Non-parametric Estimates for Dependence Functions of the... In evd: Functions for Extreme Value Distributions

## Description

Calculate non-parametric estimates for the dependence function A of the multivariate extreme value distribution and plot the estimated function in the trivariate case.

## Usage

 ```1 2 3 4``` ```amvnonpar(x = rep(1/d,d), data, d = 3, epmar = FALSE, nsloc = NULL, madj = 0, kmar = NULL, 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 `d` or a matrix with `d` 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/d,…,1/d) is returned by default since it is often a useful summary of dependence. `data` A matrix or data frame with `d` columns, which may contain missing values. `d` The dimension; an integer greater than or equal to two. The trivariate case `d = 3` is the default. `epmar` If `TRUE`, an empirical transformation of the marginals is performed in preference to marginal parametric GEV estimation, and the `nsloc` argument is ignored. `nsloc` A data frame with the same number of rows as `data`, or a list containing `d` elements of this type, for linear modelling of the marginal location parameters. In the former case, the argument is applied to all margins. The data frames are treated as covariate matrices, excluding the intercept. Numeric vectors can be given as alternatives to single column data frames. A list can contain `NULL` elements for stationary modelling of selected margins. `madj` Performs marginal adjustments. See `abvnonpar`. `kmar` In the rare case that the marginal distributions are known, specifies the GEV parameters to be used instead of maximum likelihood estimates. `plot` Logical; if `TRUE`, and the dimension `d` is three (the default dimension), the dependence function of a trivariate extreme value distribution is plotted. For plotting in the bivariate case, use `abvnonpar`. 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 \code{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`. The argument alters the way in which the function is plotted; it does not change the function definition. `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

A numeric vector of estimates. If plotting, the smallest evaluated estimate is returned invisibly.

## 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 margins.

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

The estimator plotted or calculated is a multivariate extension of the bivariate Pickands estimator defined in `abvnonpar`.

## See Also

`amvevd`, `abvnonpar`, `fgev`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```s5pts <- matrix(rexp(50), nrow = 10, ncol = 5) s5pts <- s5pts/rowSums(s5pts) sdat <- rmvevd(100, dep = 0.6, model = "log", d = 5) amvnonpar(s5pts, sdat, d = 5) ## Not run: amvnonpar(data = sdat, plot = TRUE) ## Not run: amvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3]) ## Not run: amvevd(dep = 0.6, model = "log", plot = TRUE) ## Not run: amvevd(dep = 0.6, model = "log", plot = TRUE, blty = 1) ```

### Example output

```  0.5977544 0.5804372 0.7155213 0.6422893 0.5682064 0.5757996 0.6631578
 0.5996574 0.5981655 0.6740658
```

evd documentation built on May 1, 2019, 10:11 p.m.