Poisson律熵的锐界及相关定理
Sharp Bounds on the Entropy of the Poisson Law and Related Quantities
摘要：
在计算某些泊松信道的容量的困难之一是，H（λ），平均λ的泊松分布的熵，是不是在一个简单的形式。在这项工作中，我们推导出H（λ）的上界和下界，它们是渐近紧的，易于计算。这种界限的推导只涉及简单的概率和分析工具。这补充了Knessl（1998）、Jacquet and Szpankowski（1999）和Flajolet（1999）的渐近展开式。同样的方法在二项式和泊松之间的相对熵D（n，p）上产生了严格的界限，从而改进了Harremoes和Ruzankin（2004）的工作。二项式的熵的界限也很容易遵循。
英文摘要：
One of the difficulties in calculating the capacity of certain Poisson channels is that H(lambda), the entropy of the Poisson distribution with mean lambda, is not available in a simple form. In this work we derive upper and lower bounds for H(lambda) that are asymptotically tight and easy to compute. The derivation of such bounds involves only simple probabilistic and analytic tools. This complements the asymptotic expansions of Knessl (1998), Jacquet and Szpankowski (1999), and Flajolet (1999). The same method yields tight bounds on the relative entropy D(n, p) between a binomial and a Poisson, thus refining the work of Harremoes and Ruzankin (2004). Bounds on the entropy of the binomial also follow easily.
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