Maximum-likelihood fitting for the gumbel distribution, including generalized linear modelling of each parameter.
gum.fit(xdat, ydat = NULL, mul = NULL, sigl = NULL, mulink = identity,
siglink = identity, muinit = NULL, siginit = NULL, show = TRUE,
method = "Nelder-Mead", maxit = 10000, …)A numeric vector of data to be fitted.
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.
Numeric vectors of integers, giving the columns
of ydat that contain covariates for generalized linear
modelling of the location and scale parameters repectively
(or NULL (the default) if the corresponding parameter is
stationary).
Inverse link functions for generalized linear modelling of the location and scale parameters repectively.
numeric giving initial parameter estimates. See Details section for information about default values (NULL).
Logical; if TRUE (the default), print details of
the fit.
The optimization method (see optim for
details).
The maximum number of iterations.
Other control parameters for the optimization. These
are passed to components of the control argument of
optim.
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.
An logical indicator for a non-stationary fit.
A list with components mul and sigl.
A character vector giving inverse link functions.
The convergence code, taken from the list returned by
optim. A zero indicates successful convergence.
The negative logarithm of the likelihood evaluated at the maximum likelihood estimates.
The data that has been fitted. For non-stationary models, the data is standardized.
A vector containing the maximum likelihood estimates.
The covariance matrix.
A vector containing the standard errors.
A matrix with two columns containing the maximum likelihood estimates of the location and scale parameters at each data point.
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. 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 Gumbel( mu(t)=mu0+mu1*t, sigma) is being fitted, then the initial value for mu0 is m - 0.57722 * s, and 0 for mu1.
# NOT RUN {
data(portpirie)
gum.fit(portpirie[,2])
# }
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