R: Maximum-likelihood Fitting of the Maximum of Two Gumbel...

fgumbelx {evd} | R Documentation

## Maximum-likelihood Fitting of the Maximum of Two Gumbel Distributions

### Description

Maximum-likelihood fitting for the maximum of two gumbel distributions, allowing any of the parameters to be held fixed if desired.

### Usage

    fgumbelx(x, start, ..., nsloc1 = NULL, nsloc2 = NULL, std.err = TRUE,
        corr = FALSE, method = "BFGS", warn.inf = TRUE)

### Arguments

`x` | A numeric vector, which may contain missing values.
`start` | A named list giving the initial values for the parameters over which the likelihood is to be maximized. If `start` is omitted the routine attempts to find good starting values using moment estimators.
`...` | Additional parameters, either for the fitted model or for the optimization function `optim`. If parameters of the model are included they will be held fixed at the values given (see Examples).
`nsloc1` | A data frame with the same number of rows as the length of `x`, for linear modelling of the location parameter of the first Gumbel distribution. This is not recommended as the model is already complex.
`nsloc2` | A data frame with the same number of rows as the length of `x`, for linear modelling of the location parameter of the second Gumbel distribution. This is not recommended as the model is already complex.
`std.err` | Logical; if `TRUE` (the default), the standard errors are returned.
`corr` | Logical; if `TRUE`, the correlation matrix is returned.
`method` | The optimization method (see `optim` for details).
`warn.inf` | Logical; if `TRUE` (the default), a warning is given if the negative log-likelihood is infinite when evaluated at the starting values.

### Details

For stationary models the parameter names are `loc1`, `scale1`, `loc2` and `scale2` for the location and scale parameters of two Gumbel distributions, where `loc2` must be greater or equal to `loc1`.

The likelihood may have multiple local optima and therefore may be difficult to fit properly; the default starting values use a moment based approach, however it is recommended that the user specify multiple different starting values and experiment with different optimization methods.

Using non-stationary models with nsloc1 and nsloc2 is not recommended due to the model complexity; the data also cannot be transformed back to stationarity so diagnostic plots will be misleading in this case.

### Value

Returns an object of class `c("gumbelx","evd")`.

The generic accessor functions `fitted` (or `fitted.values`), `std.errors`, `deviance`, `logLik` and `AIC` extract various features of the returned object.

The functions `profile` and `profile2d` are used to obtain deviance profiles for the model parameters. The function `anova` compares nested models. The function `plot` produces diagnostic plots.

An object of class `c("gumbelx","evd")` is a list containing at most the following components

`estimate` | A vector containing the maximum likelihood estimates.
`std.err` | A vector containing the standard errors.
`fixed` | A vector containing the parameters of the model that have been held fixed.
`param` | A vector containing all parameters (optimized and fixed).
`deviance` | The deviance at the maximum likelihood estimates.
`corr` | The correlation matrix.
`var.cov` | The variance covariance matrix.
`convergence, counts, message` | Components taken from the list returned by `optim`.
`data` | The data passed to the argument `x`.
`nsloc1` | The argument `nsloc1`.
`nsloc2` | The argument `nsloc2`.
`n` | The length of `x`.
`call` | The call of the current function.

### Warning

This function is experimental and involves optimizing over a potentially complex surface.

### See Also

`fgev`, `optim`, `rgumbelx`

### Examples

    uvdata <- rgumbelx(100, loc1 = 0, scale1 = 1, loc2 = 1, scale2 = 1)
    fgumbelx(uvdata, loc1 = 0, scale1 = 1)

[Package evd version 2.3-5 Index]