gev.parameterCI: Return Level and Shape Parameter Confidence Intervals for GEV (or GP) Distribution.

Description

Computes confidence intervals for return levels and/or shape parameters of GEV (or GP) using the profile likelihood appraoch.

Usage

gev.parameterCI(z, m, rl.xlow=NULL, rl.xup=NULL, xi.xlow=NULL, xi.xup=NULL, conf = 0.95,
    nint = 100, rl.only=FALSE, xi.only=FALSE, make.plot=FALSE)
gpd.parameterCI(z, m, conf = 0.95, nint = 100, rl.xup=NULL, rl.xlow=NULL,
    xi.xup=NULL, xi.xlow=NULL, rl.only=FALSE,
    xi.only=FALSE, make.plot=FALSE)

Arguments

object from gev.fit or gpd.fit functions of the ismev package.

m-year return level for which to calculate confidence interval.

rl.xlow

initial guess of lower limit for return level (generally should be lower than actual limit). If NULL, this function will make its own guess--it is recommended to plot the profile likelihood when finding these limits automatically (make.plot=

rl.xup

initial guess of upper limit for return level (generally should be higher than actual limit). If NULL, this function will make its own guess--it is recommended to plot the profile likelihood when finding these limits automatically (make.plot

xi.xlow

analogous to rl.xlow, but for shape parameter.

xi.xup

analogous to rl.xup, but for shape parameter.

conf

desired confidence.

nint

number of values (ret. level and/or shape parameter) to compute in trying to find confidence bounds.

rl.only

logical, if TRUE calculate only the return level confidence intervals.

xi.only

logical, if TRUE calculate only the shape parameter confidence intervals.

make.plot

logical, if TRUE plots profile likelihoods.

Value

A list with components:
upcross.levelthe maximum log-likelihood value less the associated chi-square quantile.
rla list object containing the return level characteristics. Including: the maximum likelihood estimate for the m-year return level (mle), the spline function used to estimate the profile likelihood (sfun), and the upper (up) and lower (dn) confidence limits.
xiShape parameter characteristics--analogous to rl, but no mle component.

Details

This is a fairly rough routine, and is designed mainly to work internally with the extRemes GUI dialogs. However, it can be used externally with care. It makes use of a bisection search and spline fitting in order to find where the profile likelihood crosses the horizontal line through c; the maximum log-likelihood less the associated chi-square quantile.

References

Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values, London: Springer-Verlag, 208pp.

Examples

Run this code

data(ftcanmax)
fit <- gev.fit( ftcanmax[,"Prec"])
obj <- gev.parameterCI(fit, m=550, xi.xlow=-0.1, xi.xup=0.5, make.plot=TRUE)

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