| Popis: |
This report introduces an expanded class of quantile level sets {(j-α)/(n+c), j = 1, ⋯, n} to augment the popular ones, i.e., (α = ½, c = 0) used in q-q probability plots and (α = 0, c = 1) known as the Pyke alternative, for use in data analysis graphical studies of order statistics and for tests of distribution hypotheses. The expanded class can be useful in small sample studies in which their effects can be the greatest. The corresponding test statistics have the form Tn = (max |uj ‒ (j-α)/(n+c)|, j = 1, ⋯, n) where the {uj} are the order statistics of a random sample of size n from a Uniform (0, 1) population. A sub family, called tail symmetric, is described and shown to have greater efficacy than the other members of the family. The small sample distributions of these statistics are developed using Markov Chain methodology. The computational aspects are illustrated, with n = 5 using a selected set of featured statistics. Some computational idiosyncrasies are attended to and some behavioral properties are illustrated graphically. A number of side issues are discussed. Approved for public release; distribution is unlimited. |
