Tests Based on EDF Statistics

This chapter considers tests of fit based on the empirical distribution function (EDF). The EDF is a step function, calculated from the sample, which estimates the population distribution function. From the basic definitions of the supremum statistics and the quadratic statistics given above, suitable computing formulas must be found. A second group of statistics for censored samples is of the general Cramer-von Mises type. The modifications for all the statistics were calculated from points for finite n obtained by Monte Carlo methods. Green and Hegazy have shown that slight modifications of the basic EDF statistics can improve power in tests for normality against selected alternatives. Data may appear to be discrete either because the sample genuinely arises from a discrete distribution like the Binomial or Poisson, for example, in measurements of counts, or alternatively because originally continuous data may have been grouped.