GPD Return Level Estimate and Confidence Interval for Stationary Models

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Description

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

Usage

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

Arguments

z

An object of class ‘gpdFit’.

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. Argument passed to optim. The default method is Nelder-Mead.

Details

Caution: The profile likelihood optimization may be slow for large datasets.

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

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

Examples

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x <- rgpd(5000, loc = 0, scale = 1, shape = -0.1)
## Compute 50-period return level.
z <- gpdFit(x, nextremes = 200)
gpdRl(z, period = 50, method = "delta")
gpdRl(z, period = 50, method = "profile")

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