A Note on the Optimum Spacing of Sample Quantiles from the Six Extreme Value Distributions

摘要

The extreme value distributions have many fields of application, including floods, wind speeds, earthquakes, aeronautics, naval engineering, corrosion and strength of materials. This paper deals with the estimation of an unknown location or scale parameter of an extreme value distribution by using only a few sample quantiles. Such methods are often convenient in testing procedures. The paper is particularly concerned with the optimum selection of sample quantiles from a large sample. It is shown that the problems of asymptotically optimum spacing of sample quantiles in connection with asymptotically best linear unbiased estimation of the location parameter of an extreme value distribution of Type 1 or the scale parameter of an extreme value distribution of Type 2 or 3, are essentially the same. Previous results for the scale parameter of an exponential distribution can therefore be used also for the extreme value distributions. (Author)