kerdiest (version 1.3-1)

rl: 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))

Value

A single value or an array for the estimated quantiles.

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.

Author

Graciela Estévez Pérez and Alejandro Quintela del Río

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.

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

# \donttest{
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")
# }