# dot-gpd_2D_fit: Maximum likelihood method for the generalized Pareto Model In mev: Modelling of Extreme Values

 .gpd_2D_fit R Documentation

## Maximum likelihood method for the generalized Pareto Model

### Description

Maximum-likelihood estimation for the generalized Pareto model, including generalized linear modelling of each parameter. This function was adapted by Paul Northrop to include the gradient in the `gpd.fit` routine from `ismev`.

### Usage

``````.gpd_2D_fit(
xdat,
threshold,
npy = 365,
ydat = NULL,
sigl = NULL,
shl = NULL,
siginit = NULL,
shinit = NULL,
show = TRUE,
maxit = 10000,
...
)
``````

### Arguments

 `xdat` numeric vector of data to be fitted. `threshold` a scalar or a numeric vector of the same length as `xdat`. `npy` number of observations per year/block. `ydat` matrix of covariates for generalized linear modelling of the parameters (or `NULL` (the default) for stationary fitting). The number of rows should be the same as the length of `xdat`. `sigl` numeric vector of integers, giving the columns of `ydat` that contain covariates for generalized linear modelling of the scale parameter (or `NULL` (the default) if the corresponding parameter is stationary). `shl` numeric vector of integers, giving the columns of `ydat` that contain covariates for generalized linear modelling of the shape parameter (or `NULL` (the default) if the corresponding parameter is stationary). `siglink` inverse link functions for generalized linear modelling of the scale parameter `shlink` inverse link functions for generalized linear modelling of the shape parameter `siginit` numeric giving initial value(s) for parameter estimates. If `NULL` the default is `sqrt(6 * var(xdat))/pi` `shinit` numeric giving initial value(s) for the shape parameter estimate; if `NULL`, this is 0.1. If using parameter covariates, then these values are used for the constant term, and zeros for all other terms. `show` logical; if `TRUE` (default), print details of the fit. `method` optimization method (see `optim` for details). `maxit` maximum number of iterations. `...` other control parameters for the optimization. These are passed to components of the `control` argument of `optim`.

### Details

For non-stationary fitting it is recommended that the covariates within the generalized linear models are (at least approximately) centered and scaled (i.e. the columns of `ydat` should be approximately centered and scaled).

The form of the GP model used follows Coles (2001) Eq (4.7). In particular, the shape parameter is defined so that positive values imply a heavy tail and negative values imply a bounded upper value.

### Value

a list with components

nexc

scalar giving the number of threshold exceedances.

nllh

scalar giving the negative log-likelihood value.

mle

numeric vector giving the MLE's for the scale and shape parameters, resp.

rate

scalar giving the estimated probability of exceeding the threshold.

se

numeric vector giving the standard error estimates for the scale and shape parameter estimates, resp.

trans

logical indicator for a non-stationary fit.

model

list with components `sigl` and `shl`.

character vector giving inverse link functions.

threshold

threshold, or vector of thresholds.

nexc

number of data points above the threshold.

data

data that lie above the threshold. For non-stationary models, the data are standardized.

conv

convergence code, taken from the list returned by `optim`. A zero indicates successful convergence.

nllh

negative log likelihood evaluated at the maximum likelihood estimates.

vals

matrix with three columns containing the maximum likelihood estimates of the scale and shape parameters, and the threshold, at each data point.

mle

vector containing the maximum likelihood estimates.

rate

proportion of data points that lie above the threshold.

cov

covariance matrix.

se

numeric vector containing the standard errors.

n

number of data points (i.e., the length of `xdat`).

npy

number of observations per year/block.

xdata

data that has been fitted.

### References

Coles, S., 2001. An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London.

mev documentation built on May 29, 2024, 9:10 a.m.