ABSTRACT
It is clear that information concerning extremes may be important in many types of problems. There are many properties of distributions which can be defined, and which have useful interpretations in extreme value theory. It is often useful to know the asymptotic or limiting distributions of statistics. Graphical or least squares methods can be used for estimating location-scale parameters for limiting distributions. This chapter focuses on statistical procedures for the Weibull distribution. Many variables such as lifetimes, strengths, and droughts, may correspond to minimums of positive variables such as the gamma variable, and these minimums would have a limiting type III or Weibull distribution. A very long chain is considered, the individual links are independent, and identically distributed gamma variables. Thompson discusses an example of highway traffic flow where individual cars have gamma distributed free speeds, but that group speeds correspond to the minimum or slowest driver.
