rl: Return Level Estimation

In kerdiest: Nonparametric Kernel Estimation of Distribution Function

Return Level Estimation

Description

The T-return level is defined as the value of the observed variable that can be expected to be once exceeded during a T-period of time. This is computed as the quantile of the distribution corresponding to the value F^{-1}(1-\frac{1}{T}).

Usage

rl(type_kernel = "n", vec_data, time,
          bw = PBbw(type_kernel = "n", vec_data, 2))

Arguments

type_kernel	The kernel function used. You can use four types: "e" Epanechnikov, "n" Normal, "b" Biweight and "t" Triweight. The normal kernel is used by default.
vec_data	The data sample (earthquake magnitudes, flow levels, wind speeds...).
time	A time or a vector of times for T.
bw	The bandwidth parameter. By default, he plug-in method of Polansky and Baker (2000) is used.

Details

In several scientific fields, it is of interest to estimate quantiles corresponding to a probability of exceedance. E.g., in hydrology, the T-return level x_T is defined as the value of the observed flow that can be expected to be once exceeded during a T-period of time; i.e., the quantile

x_T=F^{-1}(1-\frac{1}{T}).

It can be directly estimated by

\hat{x}_T=F_h^{-1}(1-\frac{1}{T}).

See, e.g., Quintela-del-Rio (2011), for an application to data of Salt River near Roosevelt, AZ, USA.

Value

A single value or an array for the estimated quantiles.

Author(s)

Graciela Estévez Pérez and Alejandro Quintela del Río

References

Quintela-del-Rio, A. (2011), "On bandwidth selection for nonparametric estimation in flood frequency analysis". Hydrological Processes 25, 671-678.

Quintela-del-Río, A. and Estévez-Pérez, G. (2012), "Nonparametric kernel distribution function estimation with kerdiest: an R package for bandwidth choice and applications", Journal of Statistical Software, 50(8), 1-21.

Examples

data(saltriver)
peak <- saltriver$peakflow
year <- saltriver$year
plot(year, peak, type = "l", ylab = "Annual peak flow")
## Calculating the return values for a period from 2 to 100 years
times <- seq(2,100, length.out = 100)
ret.lev <- rl(vec_data = peak, time = times)
plot(times, ret.lev, type = "l", xlab = "Years", ylab = "Flow (cumecs)",
main = "Return level Plot")

kerdiest documentation built on June 23, 2025, 5:08 p.m.