gevrRl {eva}

GEVr Return Level Estimate and Confidence Interval for Stationary Models

Description

Computes stationary m-period return level estimate and interval, using either the delta method or profile likelihood.

Usage

gevrRl(
  z,
  period,
  conf = 0.95,
  method = c("delta", "profile"),
  plot = TRUE,
  opt = c("Nelder-Mead")
)

Arguments

z

A class object returned from gevrFit. Must be a stationary fit.

period

The number of periods to use for the return level.

conf

Confidence level. Defaults to 95 percent.

method

The method to compute the confidence interval - either delta method (default) or profile likelihood.

plot

Plot the profile likelihood and estimate (vertical line)?

opt

Optimization method to maximize the profile likelihood if that is selected. The default method is Nelder-Mead.

Details

It is generally accepted that profile likelihood confidence intervals provide greater accuracy than the delta method, in particular for large return level periods. Also, by their nature, delta method confidence intervals must be symmetric which may be undesirable for return level estimation. If the original fit was Gumbel, then return levels will be for the Gumbel distribution.

Caution: The profile likelihood optimization may be slow (on the order of minutes).

Value

Estimate

Estimated m-period return level.

CI

Confidence interval for the m-period return level.

Period

The period length used.

ConfLevel

The confidence level used.

References

http://www.mas.ncl.ac.uk/~nlf8/teaching/mas8391/background/chapter2.pdf

Coles, S. (2001). An introduction to statistical modeling of extreme values (Vol. 208). London: Springer.

Examples

x <- rgevr(100, 2, loc = 0.5, scale = 1, shape = -0.3)
z <- gevrFit(x)
# Compute 250-period return level.
gevrRl(z, 250, method = "delta")