Maximumlikelihood Fitting for the GPD Model
Description
Maximumlikelihood fitting for the GPD model, including generalized linear modelling of each parameter.
Usage
1 2 3 4 
Arguments
xdat 
A numeric vector of data to be fitted. 
threshold 
The threshold; a single number or a numeric
vector of the same length as 
npy 
The number of observations per year/block. 
ydat 
A matrix of covariates for generalized linear modelling
of the parameters (or 
sigl, shl 
Numeric vectors of integers, giving the columns
of 
siglink, shlink 
Inverse link functions for generalized linear modelling of the scale and shape parameters repectively. 
siginit, shinit 
numeric giving initial value(s) for parameter estimates. If NULL, default is sqrt(6 * var(xdat))/pi and 0.1 for the scale and shape parameters, resp. If using parameter covariates, then these values are used for the constant term, and zeros for all other terms. 
show 
Logical; if 
method 
The optimization method (see 
maxit 
The maximum number of iterations. 
... 
Other control parameters for the optimization. These
are passed to components of the 
Details
For nonstationary 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 containing the following components. A subset of these
components are printed after the fit. If show
is
TRUE
, then assuming that successful convergence is
indicated, the components nexc
, nllh
,
mle
, rate
and se
are always printed.
nexc 
single numeric giving the number of threshold exceedances. 
nllh 
nsingle umeric giving the negative loglikelihood value. 
mle 
numeric vector giving the MLE's for the scale and shape parameters, resp. 
rate 
single numeric giving the estimated probability of exceeding the threshold. 
se 
numeric vector giving the standard error estiamtes for the scale and shape parameter estimates, resp. 
trans 
An logical indicator for a nonstationary fit. 
model 
A list with components 
link 
A character vector giving inverse link functions. 
threshold 
The threshold, or vector of thresholds. 
nexc 
The number of data points above the threshold. 
data 
The data that lie above the threshold. For nonstationary models, the data is standardized. 
conv 
The convergence code, taken from the list returned by

nllh 
The negative logarithm of the likelihood evaluated at the maximum likelihood estimates. 
vals 
A matrix with three columns containing the maximum likelihood estimates of the scale and shape parameters, and the threshold, at each data point. 
mle 
A vector containing the maximum likelihood estimates. 
rate 
The proportion of data points that lie above the threshold. 
cov 
The covariance matrix. 
se 
A vector containing the standard errors. 
n 
The number of data points (i.e.\ the length of

npy 
The number of observations per year/block. 
xdata 
The data that has been fitted. 
References
Coles, S., 2001. An Introduction to Statistical Modeling of Extreme Values. SpringerVerlag, London, U.K., 208pp.
See Also
gpd.diag
, optim
,
gpd.prof
, gpd.fitrange
,
mrl.plot
, pp.fit
Examples
1 2 