Infinitely Divisible Distributions, Conditions for Independence, and Central Limit Theorems

摘要

A discussion is given of some general results for a class of random vectors that often arise in the modeling of radar clutter interference. If a random variable is the sum of a large number of small, statistically independent components, it can under certain conditions be approximated by the normal distribution. When these conditions cannot be obtained, the random variable can be approximated by a member of a broader class of infinitely divisible (I.D.) random variables. Conditions for independence are developed and a new parameter defines dependence between non-normal components of two I.D. random variables. Central limit theorems for sequences of I.D. variables and sequences of sums of small independent random variables employ characterizations of normal and Poisson distributions. (Author)