Return levels

Description

Computation of return levels and confidence intervals for extreme value models.

Usage

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## S3 method for class 'rl.evmOpt'
plot(x, xlab, ylab, main, pch = 1, ptcol = 2,
  cex = 0.75, linecol = 4, cicol = 0, polycol = 15, smooth = FALSE,
  sameAxes = TRUE, type = "median", ylim = NULL, plot. = TRUE, ...)

## S3 method for class 'rl.evmSim'
plot(x, xlab, ylab, main, pch = 1, ptcol = 2,
  cex = 0.75, linecol = 4, cicol = 0, polycol = 15, smooth = FALSE,
  sameAxes = TRUE, type = "median", ylim = NULL, plot. = TRUE, ...)

## S3 method for class 'rl.evmBoot'
plot(x, xlab, ylab, main, pch = 1, ptcol = 2,
  cex = 0.75, linecol = 4, cicol = 0, polycol = 15, smooth = FALSE,
  sameAxes = TRUE, type = "median", ylim = NULL, plot. = TRUE, ...)

rl(object, M = 1000, newdata = NULL, se.fit = FALSE, ci.fit = FALSE,
  alpha = 0.05, unique. = TRUE, ...)

## S3 method for class 'evmOpt'
rl(object, M = 1000, newdata = NULL, se.fit = FALSE,
  ci.fit = FALSE, alpha = 0.05, unique. = TRUE, ...)

## S3 method for class 'evmSim'
rl(object, M = 1000, newdata = NULL, se.fit = FALSE,
  ci.fit = FALSE, alpha = 0.05, unique. = TRUE, all = FALSE,
  sumfun = NULL, ...)

## S3 method for class 'evmBoot'
rl(object, M = 1000, newdata = NULL, se.fit = FALSE,
  ci.fit = FALSE, alpha = 0.05, unique. = TRUE, all = FALSE,
  sumfun = NULL, ...)

## S3 method for class 'rl.evmOpt'
print(x, digits = 3, ...)

Arguments

x

Object passed to plot and print methods.

xlab, ylab, main, pch, ptcol, cex, linecol, cicol, polycol, smooth, sameAxes, ylim

Further arguments to plot methods.

type

For calls to plot methods for objects of class rl.evmSim or rl.evmBoot, specifies whether to use the sample mean (type="mean") or median (type="median") estimate of the return levels.

plot.

Parameter for plot method, whether to produce plots.

...

Further arguments to be passed to methods.

object

An object of class evmOpt, evmSim or evmBoot.

M

The M-observation return level is computed by the function. Defaults to M = 1000.

newdata

Data from which to calculate the return level. If not provided, the original data used to fit the model is used. Column names must match those of original data matrix used for model fitting.

se.fit

Whether or not to return the standard error of the predicted value. Defaults to se.fit = FALSE.

ci.fit

Whether or not to return a confidence interval for the predicted value. Defaults to ci.fit = FALSE. For objects of class evmOpt, if set to TRUE then the confidence interval is a simple symmetric confidence interval based on the estimated approximate standard error. For the evmSim and evmBoot methods, the confidence interval represents quantiles of the simulated distribution of the parameters.

alpha

If ci.fit = TRUE, a 100(1 - alpha)% confidence interval is returned. Defaults to alpha = 0.050.

unique.

If unique. = TRUE, predictions for only the unique values of the linear predictors are returned, rather than for every row of the original dataframe or of newdata if this latter is specified. Defaults to unique. = TRUE.

all

For the evmSim and evmBoot methods, if all = TRUE, the predictions are returned for every simulated parameter vector. Otherwise, only a summary of the posterior/bootstrap distribution is returned. Defaults to all = FALSE.

sumfun

For the evmSim and evmBoot methods, a summary function can be passed in. If sumfun = FALSE, the default, the summary function used returns the estimated mean and median, and quantiles implied by alpha.

digits

Number of digits to show when printing output.

Details

The M-observation return level is defined as the value that is expected to be exceeded only once every M observations. Thus, it is an estimate of a high quantile of the fitted distribution.

In models fit by the evm family of functions with family=gpd, only a fraction of the data is actually included in the model; the fitted GPD is a conditional model, conditioning on the threshold having been exceeded. This consideration is taken into account by rl which calculates unconditional return levels from the entire distribution of observations above and below the GPD fitting threshold.

Examples

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mod <- evm(rain, qu=.8) # daily rainfall observations
rl(mod, M=100*365) # 100-year return level

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