gev.fit: Maximum-likelihood Fitting of the GEV Distribution

In ismev: An Introduction to Statistical Modeling of Extreme Values

Description

Maximum-likelihood fitting for the generalized extreme value distribution, including generalized linear modelling of each parameter.

Usage

gev.fit(xdat, ydat = NULL, mul = NULL, sigl = NULL, shl = NULL, 
    mulink = identity, siglink = identity, shlink = identity, 
    muinit = NULL, siginit = NULL, shinit = NULL,
    show = TRUE, method = "Nelder-Mead", maxit = 10000, ...)

Arguments

xdat	A numeric vector of data to be fitted.
ydat	A 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.
mul, sigl, shl	Numeric vectors of integers, giving the columns of ydat that contain covariates for generalized linear modelling of the location, scale and shape parameters repectively (or NULL (the default) if the corresponding parameter is stationary).
mulink, siglink, shlink	Inverse link functions for generalized linear modelling of the location, scale and shape parameters repectively.
muinit, siginit, shinit	numeric of length equal to total number of parameters used to model the location, scale or shape parameter(s), resp. See Details section for default (NULL) initial values.
show	Logical; if TRUE (the default), print details of the fit.
method	The optimization method (see optim for details).
maxit	The maximum number of iterations.
...	Other control parameters for the optimization. These are passed to components of the control argument of optim.

Details

The form of the GEV used is that of Coles (2001) Eq (3.2). Specifically, positive values of the shape parameter imply a heavy tail, and negative values imply a bounded upper tail.

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).

Let m=mean(xdat) and s=sqrt(6*var(xdat))/pi. Then, initial values assigend when 'muinit' is NULL are m - 0.57722 * s (stationary case). When 'siginit' is NULL, the initial value is taken to be s, and when 'shinit' is NULL, the initial value is taken to be 0.1. When covariates are introduced (non-stationary case), these same initial values are used by default for the constant term, and zeros for all other terms. For example, if a GEV( mu(t)=mu0+mu1*t, sigma, xi) is being fitted, then the initial value for mu0 is m - 0.57722 * s, and 0 for mu1.

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 nllh, mle and se are always printed.

nllh	single numeric giving the negative log-likelihood value.
mle	numeric vector giving the MLE's for the location, scale and shape parameters, resp.
se	numeric vector giving the standard errors for the MLE's for the location, scale and shape parameters, resp.
trans	An logical indicator for a non-stationary fit.
model	A list with components mul, sigl and shl.
link	A character vector giving inverse link functions.
conv	The convergence code, taken from the list returned by optim. A zero indicates successful convergence.
nllh	The negative logarithm of the likelihood evaluated at the maximum likelihood estimates.
data	The data that has been fitted. For non-stationary models, the data is standardized.
mle	A vector containing the maximum likelihood estimates.
cov	The covariance matrix.
se	A vector containing the standard errors.
vals	A matrix with three columns containing the maximum likelihood estimates of the location, scale and shape parameters at each data point.

References

Coles, S., 2001. An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London, U.K., 208pp.

See Also

gev.diag, optim, gev.prof

Examples

data(portpirie)
gev.fit(portpirie[,2])

Example output

Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.
$conv
[1] 0

$nllh
[1] -4.339058

$mle
[1]  3.87474692  0.19804120 -0.05008773

$se
[1] 0.02793211 0.02024610 0.09825633

ismev documentation built on May 1, 2019, 9:10 p.m.