ef: Exceedance function estimation

In kerdiest: Nonparametric kernel estimation of the distribution function. Bandwidth selection and estimation of related functions.

Description

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.

Usage

ef(type_kernel = "n", vec_data, c,
 bw = PBbw(type_kernel = "n", vec_data, 2),
 Dmin = 0, Dmax = 15, size_grid = 50, lambda)

Arguments

type_kernel	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.

Value

Returns a list containing:

Estimated_values	Vector containing the estimated function.
grid	The used grid.
bw	Value of the bandwidth.

Author(s)

Graciela Estevez Perez [e-mail] and Alejandro Quintela del Rio [e-mail]

References

Orlecka-Sikora, B. (2008) Resampling methods for evaluating the uncertainty of the nonparametric magnitude distribution estimation in the probabilistic seismic hazard analysis. Tectonophysics 456, 38–51.

Quintela-del-Rio, A. (2010) On non-parametric techniques for area-characteristic seismic hazard parameters. Geophysical Journal International 180, 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 Software 50(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)

kerdiest documentation built on May 2, 2019, 3:24 a.m.