# Auxiliary functions for Survival Analysis

#' Density, distribution function, and quantile function of the reverse Gumbel
#' distribution.
#'
#' Arguments:
#' @param x, q numeric vector of quantiles.
#' @param p vector of probabilities.
#' @param location location parameter.
#' @param scale scale parameter.
#' @param lower.tail logical; if TRUE (default), probabilities are
#'   $P[X \leq x]$, otherwise $P[X > x]$.
#'
#' @author Alain Hauser <alain.hauser@math.ethz.ch>
drgumbel <- function(x, location = 0, scale = 1) {
  if (min(scale) <= 0) {
    stop("Invalid scale.")
  }
  t <- exp((x - location) / scale)
  return(t * exp(-t) / scale)
}
prgumbel <- function(q, location = 0, scale = 1, lower.tail = TRUE) {
  if (min(scale) < 0) {
    stop("Invalid scale.")
  }
  p <- 1 - exp(-exp((q - location) / scale))
  if (lower.tail) {
    return(p)
  } else {
    return(1 - p)
  }
}
qrgumbel <- function(p, location = 0, scale = 1, lower.tail = TRUE) {
  if (min(p, na.rm = TRUE) <= 0 || max(p, na.rm = TRUE) >= 1) {
    stop("`p' must contain probabilities in (0, 1).")
  }
  if (min(scale) < 0) {
    stop("Invalid scale.")
  }
  if (!lower.tail) {
    p <- 1 - p
  }
  return(location + scale * log(-log1p(-p)))
}