kerdiest (version 1.3-1)

ef: 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)

Value

Returns a list containing:

Estimated_values

Vector containing the estimated function.

grid

The used grid.

bw

Value of the bandwidth.

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.

Author

Graciela Estévez Pérez and Alejandro Quintela del Río

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.

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

# \donttest{
## 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")
# }