Fit Gumbel Distribution

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Description

Fits gumbel distribution (GEV with xi = 0) to block maxima data.

Usage

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gumbel(data, block = NA, ...)

Arguments

data

data vector. Interpretation depends on value of block: if no block size is specified then data are interpreted as block maxima; if block size is set, then data are interpreted as raw data and block maxima are calculated.

block

the block size. A numeric value is interpreted as the number of data values in each successive block. All the data is used, so the last block may not contain block observations. If the data has a times attribute containing (in an object of class "POSIXct", or an object that can be converted to that class; see as.POSIXct) the times/dates of each observation, then block may instead take the character values "month", "quarter", "semester" or "year".

...

arguments passed to optim

Details

This function is primarily intended for comparison with GEV for assessing the need for a heavy-tailed Frechet (or short-tailed Weibull) to model block maxima.

Value

An object of class "gev" describing the fit and including parameter estimates and standard errors. Fitting is carried out using maximum likelihood.

See Also

plot.gev, gev, optim, as.POSIXct

Examples

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# Fit Gumbel to maxima of blocks of 100 observations
data(bmw)
out <- gumbel(bmw, 100) 
# Fit Gumbel to the data in nidd.annual, the annual maximum water 
# levels of the River Nidd, using the "BFGS" optimization method
data(nidd.annual)
out <- gumbel(nidd.annual, method = "BFGS", control = list(maxit = 500))