The Discriminant Conditions Of Extreme Value Distribution Of Discrete Variables

Extreme value theory is an important branch of the limit theory, and it main researches random sample and the nature of extreme value of the random pro-cess and its statistical inference. Recently it has developed into statistical meth-ods of applied science which is very important, and it’s widely applied in many fields. Von Mises condition provide a sufficient condition for continuous random variables which convergence to max domain of attraction, but difficult to research the extreme value distribution of discrete variables. The main discussion of this article is the extreme distribution of discrete random variables.Based on the relationship between the rapid variation and MDA(A) and the conclusion of literature[1], I try to use the way that the largest order statistic con-vergence to the rapid variation to discuss extreme value distribution of the binomial distribution, Poisson distribution and so on. On account of the big amount of cal-culation and difficulty of several series, I use approximation expressions between the binomial distribution, Poisson distribution and normal distribution to simplify the calculation and obtain corresponding conclusions with knowledge of literature [2].