Generalized Cramér-von Mises statistics for the gamma distribution

Abstract

SUMMARY Generalized Cramér-von Mises statistics for testing for the gamma distribution with known shape parameter are investigated. It is shown that the statistics can be written as an infinite sum of uncorrelated components which are polynomial functions of the original observations. These components are shown to be related to linear functions of order statistics. Simple modifications are made when the scale parameter has to be estimated. Finally the efficiencies of the components for testing for the exponential distribution against various alternatives are considered.