关于二项分布的强偏差定理

Strong Deviation Theorems of the Binomial Distribution

利用分析方法建立了用不等式表示的用渐近平均对数似然比刻划的服从二项分布的随机变量序列的强偏差定理,作为推论得到了服从二项分布的相依随机变量序列的强大数定律.

In this paper, the notion of the logarithmic likelihood ratio, as a measure of the deviation between a sequence of arbitrary random variables and a sequence of independent random variables with the binomial distribution, is introduced. Using the concept, we obtain the strong deviation theorems represented by inequalities. Meanwhile, we get the strong laws of the large numbers for the sequence of the dependent random variables obeyed the the binomial distributions.