R: Estimate the Bivariate Peaks-Over-Threshold (POT) Model

fbvpot {extRemes} | R Documentation

## Estimate the Bivariate Peaks-Over-Threshold (POT) Model

### Description

Fit the bivariate POT model to data.

### Usage

    fbvpot(x, threshold, dep.model = "logistic", na.action = na.fail,
           init = 0.5, lower = 0, upper = 1, cutoff, parnames,
           tform = "tformRankFrechet", ...)

### Arguments

`x` | `n` by 2 matrix giving each component of the bivariate vectors to which the bivariate peaks-over-threshold (POT) model is to be fit.
`threshold` | A single number, `n` by 2 matrix, or length 2 vector. If a single number, this value will be used as the threshold over which the marginal POT models will be fit to each component variable. If an `n` by 2 matrix, then each column will be a vector of thresholds for each component variable, respectively. If a length 2 vector, then the first element is used for the threshold in fitting the POT model to the first component, and the second to the second.
`dep.model` | character string giving the name of a bivariate dependence model function. The user may make their own function; such functions must take arguments `w`, `p` and `...` and should return a a vector of the likelihood values. A second function with the same name, but ending in “LH” that takes the same input arguments, calls the other function, and returns the single numeric value giving the likelihood. Options included with this package include: `logistic` and `mixbeta`.
`na.action` | function determining how missing values should be handled. Default is to error out.
`init` | vector giving an initial guess for each parameter in the dependence model defined by `dep.model`.
`lower, upper` | Arguments to the `nlminb` function, which is used to optimize the likelihood numerically.
`cutoff` |
`parnames` | optional character vector giving the names of the parameters of the dependence model.
`tform` | character string giving the name of the function to be used to transform the component variables to the same scale. Default transforms to the Frechet scale using the rank transformation.
`...` | optional arguments to the `tform` function.

### Details

See Beirlant et al. (2004) for more about bivariate threshold exceedance modeling, as well as Coles and Tawn (1994).

### Value

A list object of class “fbvpot” with components:

`orig.data` | original matrix of the data from the x argument.
`threshold, cutoff, init, lower, upper, parnames` | Same as values passed in through the input arguments.
`Frechet.transformed.data` | matrix with the Frechet-transformed data.
`radial, angular` | vectors giving the radial and angular components, respectively.
`sorting, polar` |

`model, LH` | function giving the dependence model used and its companion likelihood function, respectively.
`model.name` | character naming the dependence model used.
`fit` | the result of nlminb giving the optimized parameter value(s).
`call` | original call to this function.
`data.name` | character string giving the name of the data used in the x argument.

### Author(s)

Dan Cooley and Eric Gilleland

### References

Beirlant, J., Y. Goegebeur, J. Segers, and J. Teugels (2004) Statistics of Extremes: Theory and Applications. Wiley, West Sussex, England, United Kingdom, 514 pp.

Coles, S. G. and J. A. Tawn (1994) Statistical methods for multivariate extremes: an application to structural design (with Discussion). Appl. Statist., 43, 1–48, doi: 10.2307/2986112.

### See Also

`logistic`, `mixbeta`, `bvpotbooter`

### Examples

    data( "SantaAna" )

    Z <- SantaAna[,3:4]

    mfit1 <- fevd( x = temp, data = Z, threshold = 36.75, type = "GP" )
    mfit2 <- fevd( x = windspeeds, data = Z, threshold = 7.09875, type = "GP" )

    fit2 <- fbvpot( x = Z, threshold = apply( Z, 2, quantile, probs = 0.95 ),
    	       tform = "tf", fit = list( mfit1, mfit2 ) )
    fit2

    plot( fit2 )

    hist( fit2 )

[Package extRemes version 2.0-12 Index]