ef | R Documentation |
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.
ef(type_kernel = "n", vec_data, c,
bw = PBbw(type_kernel = "n", vec_data, 2), Dmin = 0, Dmax = 15,
size_grid = 50, lambda)
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. |
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.
Returns a list containing:
Estimated_values |
Vector containing the estimated function. |
grid |
The used grid. |
bw |
Value of the bandwidth. |
Graciela Estévez Pérez and Alejandro Quintela del Río
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.
## 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")
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