Methods for objects of class "return_level"

Methods for objects of class "return_level" returned from gev_return.

Usage

# S3 method for class 'return_level'
coef(object, ...)

# S3 method for class 'return_level'
print(x, ...)

# S3 method for class 'return_level'
vcov(object, ...)

# S3 method for class 'return_level'
summary(object, digits = max(3, getOption("digits") - 3L), ...)

# S3 method for class 'summary.return_level'
print(x, ...)

# S3 method for class 'return_level'
confint(
  object,
  parm = 1:length(object),
  level = 0.95,
  profile = FALSE,
  mult = 2,
  faster = FALSE,
  epsilon = 1e-04,
  ...
)

Arguments

object, x

An object inheriting from class "return_level", a result of a call to gev_return. object is a named numeric vector of MLEs of return levels.

For print.summary.return_level, this is an object returned by the function summary.return_level.

...

Further arguments. Only used for print.summary.return_level to pass arguments to print.

digits

An integer. Passed to signif to round the values in the summary.

parm

A numeric vector. For which components, that is, which return levels, in object we require a confidence interval.

level

The confidence level required. A numeric scalar in (0, 1).

profile

A logical scalar. If TRUE then confidence intervals based on a profile log-likelihood are returned. If FALSE then intervals based on approximate large sample normal theory, which are symmetric about the MLE, are returned.

mult

A positive numeric scalar. Controls the increment by which the parameter of interest is increased/decreased when profiling above/below its MLE. The increment is mult * se / 100 where se is the estimated standard error of the estimator of the return level. Decreasing mult profiles at more points but will be slower.

faster

A logical scalar. If faster = TRUE then the profiling of the log-likelihood in search of a lower (upper) confidence limit is started at the corresponding symmetric lower (upper) confidence limit.

epsilon

Only relevant if profile = TRUE. A numeric vector of values that determine the accuracy of the confidence limits. epsilon is recycled to the length of the parameter vector parm.

• If epsilon[i] > 0 then this value is passed as the argument epsilon to the itp::itp function, which estimates the parameter values for which the profile log-likelihood for parameter i drops to the value that defines the confidence limits, once profiling has been successful in finding an interval within which this value lies.

• If epsilon[i] < 0 quadratic interpolation is used, which will tend to be faster.

• If epsilon[i] = 0 then linear interpolation is used, which will be faster still.

Value

print.return_level and coef.return_level: a numeric vector containing the MLEs of return return levels.

vcov.return_level: a length(object) by length(object) matrix with row and column names indicating the return periods of the return levels. The estimated variance-covariance matrix for the return levels in object. The diagonal elements give the estimated variances associated with the individual return level estimates.

summary.return_level: an object containing the original function call and a matrix of estimates of return levels and associated estimated standard errors with row names indicating the respective return periods. The object is printed by print.summary.return_level.

print.summary.return_level: the argument x is returned, invisibly.

confint.return_level: an object of class c("confint_return_level", "evmissing"). A numeric matrix with 2 columns giving the lower and upper confidence limits for each return level. These columns are labelled as (1-level)/2 and 1-(1-level)/2, expressed as a percentage, by default 2.5% and 97.5%. The row names indicate the return levels. If profile = TRUE then the returned object has extra attributes crit, level and for_plot. The latter is a named list of length parm with components named after the return periods. Each components is a 2-column numeric matrix. The first column contains values of the return level and the second column the corresponding values of the profile log-likelihood. The profile log-likelihood is equal to the attribute crit at the limits of the confidence interval. The attribute level is the input argument level.

Details

For confint.return_level, the default, epsilon = -1, should work well enough in most circumstances, but to achieve a specific accuracy set epsilon to be a small positive value, for example, epsilon = 1e-4.

See also

gev_mle and gev_return, for examples of the use of confint.return_level.

Examples

## Plymouth ozone data

# See ?gev_return for confidence intervals for return levels
fit <- gev_mle(PlymouthOzoneMaxima)
rl <- gev_return(fit, m = c(100, 200))
rl
#> 100-year level 200-year level 
#>       215.5104       228.6658 
vcov(rl)
#>                100-year level 200-year level
#> 100-year level        1123.37       1464.100
#> 200-year level        1464.10       1916.351
summary(rl)
#> 
#> Call:
#> gev_return(x = fit, m = c(100, 200))
#> 
#>                Estimate Std. Error
#> 100-year level    215.5      33.52
#> 200-year level    228.7      43.78