.gpd_2D_fit {mev} | 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,
siglink = identity,
shlink = identity,
siginit = NULL,
shinit = NULL,
show = TRUE,
method = "Nelder-Mead",
maxit = 10000,
...
)
Arguments
xdat |
numeric vector of data to be fitted. |
threshold |
a scalar or a numeric vector of the same length as |
npy |
number of observations per year/block. |
ydat |
matrix of covariates for generalized linear modelling of the parameters (or |
sigl |
numeric vector of integers, giving the columns of |
shl |
numeric vector of integers, giving the columns of |
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 |
shinit |
numeric giving initial value(s) for the shape parameter estimate; if |
show |
logical; if |
method |
optimization method (see |
maxit |
maximum number of iterations. |
... |
other control parameters for the optimization. These are passed to components of the |
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
andshl
.- link
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.