kerdiest (version 1.2)

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, T, 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... ).

T

A particular value of time, or an array of time values.

bw

The bandwidth parameter. The plug-in method of Polansky and Baker (2000) is used by default.

Value

• A single value or an array for the estimated quantiles.

Details

In several scientific fields results of interest to estimate quantiles corresponding to a probability of exceedance. For example, 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; that is, the quantile $$x_T=F^{-1}(1-\frac{1}{T}).$$ We can estimate it directly by $$\hat{x}_T=F_h^{-1}(1-\frac{1}{T}).$$ See, for instance, 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, pp. 671--678. Quintela-del-Rio, A. and Estevez-Perez, G. (2012) Nonparametric Kernel Distribution Function Estimation with kerdiest: An R Package for Bandwidth Choice and Applications, Journal of Statistical Software 50(8), pp. 1-21. URL http://www.jstatsoft.org/v50/i08/.

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
 T<-seq(2,100, length.out=100)
ret.lev<-rl(vec_data=peak, T=T)
plot(T, ret.lev, type="l", xlab="years", ylab="Flow (cumecs)", 
main="Return level Plot")