RlargFit {fExtremes} | R Documentation

## Modelling the Order Statistic Model

### Description

A collection and description of functions to model the Order Statistic Model by maximum likelihood approximation based on R's 'ismev' package. The parameter estimation allows to include generalized linear modelling of each parameter.

The functions are:

`gpdglmFit` | fits empirical or simulated data to the distribution,
`print` | print method for a fitted GPD object of class ...,
`plot` | plot method for a fitted GPD object,
`summary` | summary method for a fitted GPD object,
`gevglmprofPlot` | profile log-likelihoods for return levels,
`gevglmprofxiPlot` | profile log-likelihoods for shape parameters.

### Usage

    rlargFit(x, r = dim(x)[2], y = NULL, mul = NULL, sigl = NULL,
        shl = NULL, mulink = identity, siglink = identity, shlink = identity,
        method = "Nelder-Mead", maxit = 10000, ...)

    ## S3 method for class 'rlargFit':
    print(x, ...)
    ## S3 method for class 'rlargFit':
    plot(x, which = "all", ...)
    ## S3 method for class 'rlargFit':
    summary(object, doplot = TRUE, which = "all", ...)

### Arguments

`doplot` | a logical. Should the results be plotted?
`maxit` | [rlargFit] - the maximum number of iterations.
`method` | [rlargFit] - the optimization method (see `optim` for details).
`mul, sigl, shl` | [rlargFit] - 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` | [rlargFit] - inverse link functions for generalized linear modelling of the location, scale and shape parameters repectively.
`object` | [summary] - a fitted object of class `"rlargFit"`.
`r` | [rlargFit] - the largest `r` order statistics are used for the fitted model.
`x` | [rlargFit] - a numeric matrix of data to be fitted. Each row should be a vector of decreasing order, containing the largest order statistics for each year (or time period). The first column therefore contains annual (or period) maxima. Only the first `r` columns are used for the fitted model. By default, all columns are used. If one year (or time period) contains fewer order statistics than another, missing values can be appended to the end of the corresponding row. [print][plot] - a fitted object of class `"rlargFit"`.
`y` | [rlargFit] - 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 number of rows of `x`.
`which` | [print][plot][summary] - a logical for each plot, denoting which plots should be created.
`...` | [rlargFit][plot] - control parameters and plot parameters optionally passed to the optimization and/or plot function. Parameters for the optimization function are passed to components of the `control` argument of `optim`.

### 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).

### 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.

`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.
`r` | The number of order statistics used.

For stationary models four plots are initially produced; a probability plot, a quantile plot, a return level plot and a histogram of data with fitted density. Then probability and quantile plots are produced for the largest `n` order statistics. For non-stationary models residual probability plots and residual quantile plots are produced for the largest `n` order statistics.

### Author(s)

Alec Stephenson for the code implemented from R's ismev package,
Stuart Scott for the original code, and Diethelm Wuertz for this R-port.

### References

Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer.

### Examples

    ## SOURCE("fExtremes.54D-RlargFit")

    ## Use Venice Data:
       data(venice)

    ## Fit for the order statistic model:
       xmpExtremes("Start: Parameter Fit for Order Statistics Model > ")
       fit = rlargFit(venice[, 2:4], r = 3)
       fit

    ## Summarize Results:
       xmpExtremes("Next: Diagnostic Analysis > ")
       summary(fit)

[Package fExtremes version 221.10065 Index]