正格子点上L族的若干注记

Some Notes on the Positive Lattice Long-Tailed Family

为了获得重尾分布子族L族的相关性质和结果,本文采用数学归纳法,给出了正格子点上L族的独立同分布列(i.i.d.)Poisson逼近的等价条件及判别该列能否Poisson逼近的一个方法,它比Embrechts等给出的检验方法更简洁.另一方面,给出了正格子点上L族的可加性的一个特别的证明.

In order to obtain some properties of Long-tailed family, this paper uses mathematical induction, gives the equivalent condition of Possion approximation of i. i.d.r.v, s in the positive lattice Longtailed family, hence obtains a method, which can check whether i. i.d.r.v, s in the positive lattice Longtailed family can be Poisson approximated. This method is more concise than that in Embrechts et al. On the other hand, we give a special proof of the additivity of the positive lattice Long-tailed family.