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

Description Usage Arguments Details Value Examples

estim_farr.wexp returns an object of class ("farrfit_wexp", "farrfit") which contains the results of the estimation of the far assuming W ~ exp(theta).

estim_farr.wexp(theta_hat, sigma_theta_hat, rp)

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

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

`theta_hat`	the value of the estimated theta. The estimation of theta is made assuming W ~ exp(theta). This vector is provided by the function `estim_theta.wexp`
`sigma_theta_hat`	the value the estimated standard devitation of `theta_hat` this vector is provided by the function `estim_theta.wexp`
`rp`	the return periods for which the far is to be estimated.
`x`	an object of class (`"farfit"`)
`...`	additional arguments for the plot.

This function returns an estimate of the 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.

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 ("farrfit_wexp", "farrfit"). It is a list containing the following elements:

rp: the return periods for which the far is to be estimated.
farr_hat: the estimated far for each return period rp
sigma__hat: the standard deviation of the estimator of the far assuming asymptotic gaussianity and obtained via the delta-method from sigma_theta_hat

 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)
 # parametric estimation of far with exponential distribution for theta
 theta_fit <- estim_theta.wexp(x = x, z = z)
 # Check fit for W ~ exp(theta)
 hist(theta_fit)
 ecdf(theta_fit)
 qqplot(theta_fit)

 # Estimate the far
 farr_fit.exp <- estim_farr.wexp(theta_hat = theta_fit$theta_hat,
  sigma_theta_hat = theta_fit$sigma_theta_hat,
  rp = rp)
 print(farr_fit.exp)
 ylim <- range(boundFrechet, farr_fit.exp$farr_hat)
 plot(farr_fit.exp, ylim = ylim, main = "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)