R/elnorm.R

In AntoineUC/Expectrem: Bias-reduced estimation of extreme value index and extreme quantiles, expectiles and Expected Shortfalls

elnorm=function (probs, mu = 0, sigma = 1, start.pt="quantile", tol=1e-08, maxiter=100, x0=NULL) 
{
  
  if (min(probs) <= 0 || max(probs) >= 1) {
    stop("only asymmetries between 0 and 1 allowed.")
  }
  
  if (sigma <= 0) {
    stop("sigma must be positive.")
  }
  
  if (start.pt != "mean" && start.pt != "quantile" && start.pt != "custom") {
    stop("start.pt may be either custom, mean or quantile.")
  }
  
  if(start.pt=="mean"){
    e=rep(exp(mu+sigma^2/2), length(probs))
  }
  
  if(start.pt=="quantile"){
    e=qlnorm(probs, meanlog = mu, sdlog = sigma)
  }
  
  if(start.pt=="custom"){
    if(length(x0) != length(probs)){
      stop("x0 and probs must have the same length.")
    }
    e=x0
  }
  
  gap=1
  i=1
  while (gap >= tol && i<=maxiter) {
    e1 = exp(mu+sigma^2/2)*((2*probs-1)*(1-(pchisq(2 * ((log(e)-mu-sigma^2)/(sqrt(2)*sigma))^2, 1) * sign(((log(e)-mu-sigma^2)/(sqrt(2)*sigma)))))+2*(1-probs))/((2*probs-1)*(1-(pchisq(2 * ((log(e)-mu)/(sqrt(2)*sigma))^2, 1) * sign(((log(e)-mu)/(sqrt(2)*sigma)))))+2*(1-probs))
    gap=max(abs(e1-e),na.rm=T)
    e=e1
    i=i+1
  }
  if(i>maxiter){
    warning("Warning: maximum of iterations reached !")
  }
  return(e)
}