We compute the exceedance probability, that is, the probability that a
specified value c (a magnitude of a seismic event, a flow level... )
will be exceeded in D time units.
The kernel function. 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 speed...)
c
The concrete level in which we want to compute the exceedance probability.
bw
The bandwidth parameter. The plug-in method of Polansky and Baker (2000) is
used by default.
Dmin
Minimum value for D time units (years, days... ). Default is Dmin=0.
Dmax
Maximum value for D time units (years, days... ). Default is Dmax=15.
size_grid
Length of a grid in which we compute the exceedance function. The size is
50 by default.
lambda
The mean activity rate.
Details
The exceedance function is usually calculated assuming that the occurrence process
of events follows a Poisson one. In this case, the exceedance function, that is, the
probability of an specific value c is calculated as
R(c,D) = 1- exp(-λ D(1-F_h(c)).
See, for example, Orlecka-Sikora (2008) or Quintela del Rio (2010) for earthquake
data applications.
Orlecka-Sikora, B. (2008) Resampling methods for evaluating the uncertainty of the
nonparametric magnitude distribution estimation in the probabilistic seismic hazard
analysis. Tectonophysics456, 38–51.
Quintela-del-Rio, A. (2010) On non-parametric techniques for area-characteristic
seismic hazard parameters. Geophysical Journal International180,
pp. 339–346.
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
# Working with earthquake data. We use the catalogue of the National
# Geographic Institute (IGN) of Spain and select the data of the Northwest
# of the Iberian Peninsula.
data(nwip)
require(chron)
require(date)
# we consider the data with magnitude greater than 3
mg<-nwip$magnitude[nwip$magnitude>3.0]
x1<-nwip$year
x2<-nwip$month
x3<-nwip$day
ys<-paste(x1,x2,x3)
earthquake_date<-as.character(ys)
y1s<-as.date(earthquake_date, order = "ymd")
# we compute the total number of years
y2s<-as.POSIXct(y1s)
z<-years(y2s)
n.years<-length(levels(z))
# the mean rate of earthquakes per year
lambda<-length(mg)/n.years
## Not run:
# we estimate the exceedance probability for a value of the
# the magnitude = 4
est<-ef(vec_data=mg, m_c=4, lambda=lambda)
plot(est$grid, est$Estimated_values, type="l",
xlab="years", ylab="Probability of Exceedance")
## End(Not run)