gpd function

Fit Generalized Pareto Model

Returns an object of class "gpd" representing the fit of a generalized Pareto model to excesses over a high threshold.

gpd(data, threshold = NA, nextremes = NA, method = c("ml", "pwm"),
    information = c("observed", "expected"), ...)

Arguments

• data: data vector
• threshold: a threshold value (either this or nextremes must be given but not both)
• nextremes: the number of upper extremes to be used (either this or threshold must be given but not both)
• method: whether parameters should be estimated by the maximum likelihood method "ml" or the probability-weighted moments method "pwm"
• information: whether standard errors should be calculated with "observed" or "expected" information. This only applies to the maximum likelihood method; for the probability-weighted moments method "expected" information is used if possible
• ...: arguments passed to optim

Returns

An object of class "gpd" describing the fit and including parameter estimates and standard errors.

Details

The function uses the general purpose optimization function optim when method = "ml" is chosen.

References

Parameter and quantile estimation for the generalized Pareto distribution, JRM Hosking and JR Wallis, Technometrics 29 (3), pages 339-349, 1987.

See Also

plot.gpd, shape, quant, optim

Examples

data(danish)
out <- gpd(danish, 10) 
# Fits GPD to excess losses over 10 for the Danish
# fire insurance data