Testing independence by means of the empirical probability generating function

Abstract

The notion of independence is one of the most important statistical concepts. While lots of independence tests are made for the continuous random variable, there are not many designed for count data. Here we introduce several novel classes of independence tests specially designedfor count data, based on probability generating function (PGF). We present their asymptotic properties and demonstrate their competitiveness through the results of a wide empirical study. Finally, the proposed tests are illustrated on real data examples.