(20) Stanley L. Sclove. Some aspects of inference for multivariate infinitely divisible distributions. Statistics & Decisions 1(1983), 305-321.
Measurement of dependence in the infinitely divisible class of multivariate distributions, based on developments in probability theory for that class, is discussed. It has been shown that pairwise independence is equivalent to mutual independence in this class. When the infinitely divisible variables contain no normal component (in particular, when they are discrete), the cumulant of order (2,2) can be used as a measure of pairwise dependence; when a normal component is present, the appropriate measure also involves the covariance. Results for testing independence of infinitely divisible random variables are discussed. A method of testing normality against infinitely divisible alternatives is given.