boot_farr_fit.wexp: Parametric estimation of the far from bootstrap samples of...
In thaos/farr: Computation of the Fraction of Attributable Risk for Records

Description Usage Arguments Details Value Examples

boot_farr_fit.wexp returns an object of class ("boot_farrfit.wexp", "boot_farrfit", "farrfit") which contains the estimates of the far for each bootstrap sample and for different return periods rp

1	boot_farr_fit.wexp(theta_boot, rp)

`theta_boot`	the results obtained from the function `boot_theta_fit.wexp`.
`rp`	the return periods for which theta is to be estimated.

This function returns bootstrap estimates of far, the fraction of attributable risk for records, as defined in Naveau et al (2018). This estimation is made assuming that W = - log(G(Z)) follows an exponentional distribution: W ~ exp(theta). G denotes the Cumulative Distribution Function of the counterfactual variable X. The far is estimate from the bootstrap samples of theta that are obtained by resampling bootstrap. The first bootrtrap sample corresponds to the original dataset of x and y.

For the full reference, see : Naveau, P., Ribes, A., Zwiers, F., Hannart, A., Tuel, A., & Yiou, P. Revising return periods for record events in a climate event attribution context. J. Clim., 2018., https://doi.org/10.1175/JCLI-D-16-0752.1

An object of class ("boot_farrfit.wexp", "boot_farrfit", "farrfit"). 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 <- frechet_lim(sigma = sigmaF, xi = 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)
 # Resampling bootstrap for the estimation of far assuming an exponential distribution for theta
 theta_boot.exp <- boot_theta_fit.wexp(x = x, z = z, B = 10)

 # Estimate the far from the bootstrap samples of theta
 boot_farr.exp <- boot_farr_fit.wexp(theta_boot = theta_boot.exp$theta_boot , rp = rp)
 confint(boot_farr.exp)
 print(boot_farr.exp)
 ylim <- range(boundFrechet, boot_farr.exp)
 plot(boot_farr.exp, ylim = ylim, main = "boot far exponential")
 # Theoretical for in this case (Z = sigmaF * X  with X ~ Frechet)
lines(rp, frechet_farr(r = rp, sigma = sigmaF, xi = xiF), col = "red", lty = 2)
 abline(h = boundFrechet, col = "red", lty = 2)