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}).
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.
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.
Value
A single value or an array for the estimated quantiles.
Quintela-del-Rio, A. (2011) On bandwidth selection for nonparametric estimation
in flood frequency analysis. Hydrological Processes25,
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 Software50(8), pp. 1-21.
URL http://www.jstatsoft.org/v50/i08/.
Examples
data(saltriver)
peak<-saltriver$peakflow
## Not run:
year<-saltriver$year
plot(year,peak, type="l",ylab="Annual peak flow")
## End(Not run)
# 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)
## Not run:
plot(T, ret.lev, type="l", xlab="years", ylab="Flow (cumecs)",
main="Return level Plot")
## End(Not run)