ef: Exceedance Function Estimation

In kerdiest: Nonparametric Kernel Estimation of Distribution Function

Exceedance Function Estimation

Description

Computes the exceedance probability, i.e., 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 0.
Dmax	Maximum value for D time units (years, days... ). Default is 15.
size_grid	Length of a grid in which we compute the exceedance function. By default, 50.
lambda	The mean activity rate.

Details

The exceedance function is usually calculated assuming that event occurrence follows a Poisson process. In this case, the exceedance function, i.e., the probability of an specific value c is calculated as

R(c,D) = 1 - exp(-\lambda D(1-F_h(c)).

See, e.g., 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 Estévez Pérez and Alejandro Quintela del Río

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 nonparametric techniques for area-characteristic seismic hazard parameters", Geophysical Journal International, 180, 339-346.

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

## 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)
## The data with magnitude greater than 3 are considered
mg <- nwip$magnitude[nwip$magnitude > 3.0]
x1 <- nwip$year
x2 <- nwip$month
x3 <- nwip$day
ys <- paste(x1, x2, x3)
earthquake_date <- as.character(ys)
y1s <- as.date(earthquake_date, order = "ymd")
## Computation of the total number of years
y2s <- as.POSIXct(y1s)
z <- years(y2s)
n.years <- length(levels(z))
## Mean rate of earthquakes per year
lambda <- length(mg)/n.years
## Estimation of the exceedance probability for magnitude = 4
est <- ef(vec_data = mg, c = 4, lambda = lambda)
plot(est$grid, est$Estimated_values, type = "l", xlab = "Years",
  ylab = "Probability of Exceedance")

kerdiest documentation built on June 23, 2025, 5:08 p.m.