boot_theta_fit.wexp: Parametric estimation of theta under W ~ exp(theta) in...
In thaos/farr: Computation of the Fraction of Attributable Risk for Records

Description Usage Arguments Details Value Examples

estim_theta.wexp returns a list which contains the bootstrap estimates of theta assuming W ~ exp(theta).

1	boot_theta_fit.wexp(x, z, B = 100)

`x`	the variable of interest in the counterfactual world.
`z`	the variable of interest in the factual world.
`B`	the number of bootstrap samples to draw.

This function returns bootstrap estimates of theta as defined in Naveau et al (2018) that is used to estimate the far, the fraction of attributable risk for records (with boot_farr_fit.wexp). 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 bootstrap samples of theta 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 a list containing the following elements:

theta_boot: a vector with the estimates of theta for each bootstrap sample
xboot: a list where each element contains the bootstrap sample for x
zboot: a list where each element contains the bootstrap sample for z

 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 the 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)