Limiting forms of the frequency distribution of the largest or smallest member of a sample

Summary The limiting distribution, when n is large, of the greatest or least of a sample of n , must satisfy a functional equation which limits its form to one of two main types. Of these one has, apart from size and position, a single parameter h , while the other is the limit to which it tends when h tends to zero. The appropriate limiting distribution in any case may be found from the manner in which the probability of exceeding any value x...