Abstract
An auxiliary statistic is defined for the largest data of a sample using the sample mean and standard deviation. The 5% and 95% nonexceedance levels of this statistic are employed for rejection of distribution fitting to the sample, and these nonexceedance levels are formulated for the Fisher-Tippett I and II, the Weibull, and the log-normal distributions by means of Monte Carlo simulations with a minimum of 10000 samples for each combination of sample size, censoring rate, and distribution functions. The new rejection criteria are effectively applied for the extreme data of annual maximum wind speed at 128 sites, annual maxima of daily rainfall at 58 sites, and peak storm wave heights at 29 sites. The population distributions for these extreme data emerge through this analysis.
