Robust confidence bounds for extreme upper quantiles

Four related methods are discussed for obtaining robust confidence bounds for extreme upper quantiles of the unknown distribution of a positive random variable. These methods are designed to work when the upper tail of the distribution is neither too heavy nor too light in comparison to the exponential distribution. An extensive simulated study is described, which compares the performance of nominal 90% upper confidence bounds corresponding to the four methods over a wide variety of distributions having light to heavy upper tails, ranging from a half-normal distribution to a heavy-tailed lognormal distribution.