We prove a Bernstein-type bound for the difference between the average of negative log-likelihoods of independent discrete random variables and the Shannon entropy, both defined on a countably infinite alphabet. The result holds for the class of discrete random variables with tails lighter than or on the same order of a discrete power-law distribution. Most commonly-used discrete distributions such as the Poisson distribution, the negative binomial distribution, and the power-law distribution itself belong to this class. The bound is effective in the sense that we provide a method to compute the constants in it.

翻译：我们证明伯恩斯坦型与独立离散随机变量的负对数分布值和香农通则分布值之间的差值是分界的,两者的定义都是可计算到的无限字母。结果为尾部比离散功率法分布更轻或顺序相同的离散随机变量类别。最常用的离散分布,如Poisson分布、负二元分布和功率法分布本身,属于该类别。从我们提供计算其常数的方法的意义上来说,约束是有效的。