boot_FAR_fit.emp: Empirical estimation of the FAR from bootstrap samples
In thaos/farr: Computation of the Fraction of Attributable Risk for Records

Description Usage Arguments Details Value Examples

boot_FAR_fit.emp returns an object of class ("boot_FARfit.emp", "boot_FARfit", "FARfit") which contains the estimates of the FAR for each bootstrap sample and for different return periods rp

boot_FAR_fit.emp(x, z, u, B = 100)

## S3 method for class 'FARfit'
print(x, ...)

## S3 method for class 'FARfit'
plot(x, ...)

`x`	the variable of interest in the counterfactual world.
`z`	the variable of interest in the factual world.
`u`	the thresholds used to define the events.
`B`	the number of bootstrap samples to draw.
`...`	additional arguments for the plot.

This function returns bootstrap empirical estimates of FAR, the fraction of attributable risk where events are defined in terms of a threshold exceendance. The FAR is estimate from the bootstrap samples of the data x and z that are obtained by resampling bootstrap. The first bootstrap sample corresponds to the original dataset of x and y.

An object of class ("boot_FARfit.emp", "boot_FARfit", "FARfit"). It is a matrix where each columm contains the FAR estimated for the returns periods rp for a given bootstrap sample.

 library(evd)

 muF <-  1; xiF <- .15; sigmaF <-  1.412538 #  cst^(-xiF) # .05^(-xi1);
 # asymptotic limit for the far in this case with a Frechet distributiom
 boundFrechet <- 1 - sigmaF^(-1/xiF)
 # sample size
 size <- 100
 # level=.9
 set.seed(4)
 z = rgev(size, loc = (sigmaF), scale = xiF * sigmaF, shape = xiF)
 x = rgev(length(z), loc=(1), scale = xiF, shape=xiF)

 rp = seq(from = 2, to = 30, length = 200)
 u  = qgev(1 - (1 / rp),loc = muF, scale = xiF, shape = xiF)

 # Resampling bootstrap for the empirical estimation of the FAR
 boot_FAR.emp <- boot_FAR_fit.emp(x = x, z = z, u = u, B = 10)
 print(boot_FAR.emp)
 confint(boot_FAR.emp)

 ylim <- range(boundFrechet, boot_FAR.emp)
 plot(boot_FAR.emp, ylim = ylim, main = "boot FAR empirical")
 # Theoretical FAR for in this case (Z = sigmaF * X  with X ~ Frechet)
 lines(rp, frechet_FAR(u = u, sigma = sigmaF, xi = xiF), col = "red", lty = 2)
 abline(h = boundFrechet, col = "red", lty = 2)