estim_theta.wexp: Parametric estimation of theta under H0: W ~ exp(theta)
In thaos/farr: Computation of the Fraction of Attributable Risk for Records

Description Usage Arguments Details Value Examples

estim_theta.wexp returns an object of class ("thetafit_wexp", "thetafit") which contains the results of the estimation of theta and of the fit of W ~ exp(theta).

estim_theta.wexp(x, z)

## S3 method for class 'thetafit_wexp'
hist(x, ...)

## S3 method for class 'thetafit_wexp'
qqplot(x, ...)

## S3 method for class 'thetafit_wexp'
ecdf(x, ...)

`x`	the variable of interest in the counterfactual world.
`z`	the variable of interest in the factual world.
`...`	additional arguments for the plot.

This function returns an estimate of theta as defined in Naveau et al (2018) that is used to estimate the far, the fraction of attributable risk for records (with estim_farr.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.

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 ("thetafit_wexp", "thetafit"). It is a list containing the following elements:

theta_hat: the estimate of theta
sigma_theta_hat: the standard deviation of the estimator of theta assuming asymptotic gaussianity and obtained via the delta-method
W: the estimate of W
co_test: the result of the Cox and Oakes test to test whether W follows an exponential distribution

 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)